M.Sc. in Agricultural Statistics

 M.Sc. in Agricultural Statistics

AGRICULTURAL STATISTICS

 Course Structure - at a Glance

 

COURSE TITLE 

• ELEMENTARY STATISTICAL METHODS 
• STATISTICAL METHODS FOR RESEARCH WORKERS 
• STATISTICAL METHODS FOR BIOLOGY          
• EXPERIMENTAL DESIGN FOR RESEARCH WORKERS 
• STATISTICAL METHODS FOR SOCIAL SCIENCES 
• TIME SERIES ANALYSIS 
• LINEAR PROGRAMMING 
• ECONOMETRICS 
• BIOMETRICAL GENETICS 

 

M. Sc. (Agricultural Statistics)

• MATHEMATICAL METHODS-I 
• MATHEMATICAL METHODS-II 
• PROBABILITY THEORY 
• STATISTICAL METHODS 
• STATISTICAL INFERENCE  
• MULTIVARIATE ANALYSIS 
• DESIGN OF EXPERIMENTS 
• SAMPLING TECHNIQUES 
• STATISTICAL GENETICS 
• REGRESSION ANALYSIS 
• STATISTICAL COMPUTING 
• TIME SERIES ANALYSIS 
• ACTUARIAL STATISTICS 
• BIOINFORMATICS 
• ECONOMETRICS 
• STATISTICAL QUALITY CONTROL 
• OPTIMIZATION TECHNIQUES 
• DEMOGRAPHY 
• STATISTICAL METHODS FOR LIFE SCIENCES 
• STATISTICAL ECOLOGY 
• MASTER'S SEMINAR 
• MASTER'S RESEARCH 

 

Note:  

• STAT 551 and STAT 552 are supporting courses.  These are compulsory for all the students of Agricultural Statistics.  
• STAT  560  -  STAT  569  are  core  courses  to  be  taken  by  all  the  students  of  Agricultural Statistics.  
• STAT 591 and STAT 599 are compulsory for all the students of Agricultural Statistics.  
• A  student  has  to  take  a  minimum  of  36  credits  course  work,  excluding  the  supporting  courses, seminar and research.  

 

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Ph. D. (Agricultural Statistics)

• ADVANCED STATISTICAL COMPUTING  
• SIMULATION TECHNIQUES  
• ADVANCED STATISTICAL METHODS  
• ADVANCED STATISTICAL INFERENCE  
• ADVANCED DESIGN OF EXPERIMENTS  
• ADVANCED SAMPLING TECHNIQUES  
• ADVANCED STATISTICAL GENETICS  
• STATISTICAL MODELING  
• ADVANCED TIME SERIES ANALYSIS  
• STOCHASTIC PROCESSES  
• SURVIVAL ANALYSIS  
• ADVANCED BIOINFORMATICS  
• ADVANCED ECONOMETRICS  
• RECENT ADVANCES IN THE FIELD OF  SPECIALIZATION 
• DOCTORAL SEMINAR I 
• DOCTORAL SEMINAR II 
• DOCTORAL RESEARCH  

 

Note:  

• STAT 601 and STAT 602 are supporting courses. These are compulsory for all the students of Agricultural Statistics. 
• STAT  691,  STAT  692,  STAT  651  and  STAT  699  are  compulsory  for  all  the students of Agricultural Statistics.
• A  student  has  to  take  a  minimum  of  18  credits  course  work,  excluding  the supporting courses, seminar and research. 
• A student has to take two seminars.

 

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Elementary Statistical Methods (For those students who do not have sufficient statistical background)

• Probability  :  Elementary concepts of probability; Addition theorem; Conditional Probability; Multiplication theory; Independence of events. 
• Statistical Methods  :  Population and its parameters; Sample and its statistics; Frequency distribution; Graphical representation; Measures of central tendency; Measures of dispersion; Moments; Simple correlation and regression. 
• Probability Distributions  :  Binomial; Poisson & Normal 
• Sample Survey  :  Elementary concept; Advantages of sample survey over census; Simple random sampling (SRS); SRSWR and SRSWOR; Drawing of random sample & estimation of average, total etc.; Sampling and non-sampling errors; Concept of stratified random sampling. 
• Design of Experiments  :  One way and two way classification (orthogonal); Principles of design; Uniformity trial and fertility contour map; Lay-out and analysis of CRD, RBD and LSD. 
• Tests of Significance  :  Hypotheses; Two types of errors; Exact small sample tests: z, t, χ2 and F-tests. 
• Practicals  :  Based on above topics. 

 

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Statistical Methods for Research Workers

• Probability  :  Elementary concepts of probability; Addition theorem; Conditional Probability; Multiplication theory; Independence of events. 
• Statistical Methods  :  Population and its parameters; Sample and its statistics; Frequency distribution; Graphical representation; Measures of central tendency; Measures of dispersion; Moments; Simple correlation and regression. 
• Probability Distributions  :  Binomial; Poisson & Normal 
• Sample Survey  :  Elementary concept; Advantages of sample survey over census; Simple random sampling (SRS); SRSWR and SRSWOR; Drawing of random sample & estimation of average, total etc.; Sampling and non-sampling errors; Concept of stratified random sampling. 
• Design of Experiments  :  One way and two way classification (orthogonal); Principles of design; Uniformity trial and fertility contour map; Lay-out and analysis of CRD, RBD and LSD. 
• Tests of Significance  :  Hypotheses; Two types of errors; Exact small sample tests: z, t, χ2 and F-tests. 
• Practicals  :  Based on above topics. 

 

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Statistical Methods for Research Workers

• Probability and 
• Distribution  :  Preliminaries; Bayes' theorem; Repeated trials; Random variable- Mathematical expectation and its laws; variance, covariance etc.; Distribution: Binomial, Poisson, Normal. 
• Statistical Methods  :  Rank correlation; Correlation ratio; Intra-class correlation; Multiple Regression involving three variables; Multiple and partial correlation co-efficients; Stepwise multiple regression analysis; Concept of auto-correlation function (ACF). 
• Tests of Significance  :  t, F, χ2 -tests and large sample tests; Confidence intervals; Transformation of Variables: Z-transformation. 
• Sample Survey  :  Stratified random sampling; Systematic sampling and cluster sampling. 
• Design of Experiments  :  LSD; Uses of repeated Latin squares; Missing plot techniques in RBD and LSD; Split-plot design; Multiple comparison tests. 
• Practicals  :  Based on above topics. 

 

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Statistical Methods for Biology

• Probability and 
• Distribution  :  Random variable and its expectation, variance etc., Binomial Poisson, Normal, Negative Binomial and Log normal distributions. 
• Statistical Methods  :  Multiple  and  partial  correlation;  Multiple  regression; 
• Reproduction and mortality rates and their estimation; Techniques for estimation of population number and growth. 
• Tests of Significance  :  Z, t, F and  χ2 -tests. 
• Design of Experiments  :  CRD, RBD and LSD and Split-plot design; Multiple comparison tests; Missing plot techniques in RBD and LSD; Elementary bio-assay and probit analysis. 
• Practicals  :  Based on above topics. 

 

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Experimental Design for Research Workers

• Uniformity trails  :  Size and shape of pots and blocks; Lay-out and analysis of CRD and RBD; Use of Repeated LSD's; Efficiency of blocking; Missing plot techniques and analysis of covariance in RBD and LSD Multiple comparison tests. 
• Factorial Experiments   :  Interpretation of main effects and interaction; Orthogonality and partitioning of degrees of freedom; Analysis of 22, 23, 32 experiments; Concept of confounding and analysis of some confounded factorial experiments; Split plot and strip plot designs; Transformations; Analysis of groups of experiments.  
• Practicals  :  Based on above topics. 

 

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Statistical Methods for Social Sciences

• Introduction  :  Frequency distribution; Principles governing their formation and standard distributions. 
• Concept of Sampling  :  SRS and stratified random sampling; Sampling and nonsampling errors and their remedial measures. 
• Praticals : Based on above topics. 
• Tests of Significance  :  t, F, χ2 -tests and large sample tests; Confidence intervals; 
• Transformation of Variables; Z-transformation; Distributionfree statistics- run test, sign test; Wilcoxon sign-rank test, Mann-Whitney U-test; Wald – Wolfowitz run test; Median test etc. 
• Statistical Methods  :  Simple and multiple regression and prediction equations. 
• Application of 
• Multivariate Analysis  :  Factor analysis, Cluster analysis; Discriminant function and D2 statistics; Principal component analysis. 

 

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Time series Analysis

• Time series and its components; Estimation/Elimination of different components; Variate-difference method. Concept of harmonic analysis; Correlogram and periodogram analysis; Introduction of spectral analysis; Economic application of multivariate time serice; Forecasting: Concept and different methods. 
• Practical :  Based on above topics 

 

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Linear Programming

• Convex sets; Programming problems; Graphical methods and simplex method for solution;  Duality in liner programming; Revised simplex and dual simplex method; Transportation and assignment problems. Introduction to integer programming; Quadratic programming and their application and uses. Elements of game theory; two person-zero-sum game; Relationship between game theory and linear programming. 
• Practical:  Based on above topics  

 

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Econometrics

• Classical Linear Regression Models  :  Assumptions;  BLUE  and  least  square estimates  and  their  properties;  Prediction problems. 
• Autocorrelation and Heteroscedasticity  :  Definition; Causes of such problems and their remedies. 
• Multicollinearity  :  The  meaning  and  consequences  of  its existence; Tests of identifying the existence of multicollinearity;  Remedies  necessary  for analysis. 
• Simultaneous Equation Models  :  Definitions;  OLS;  ILS,  2  SLS  methods  and their applications. 
• Practicals  :  Based on above topics.

 

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Biometrical Genetics

• Estimation  of  linkage  from  back-cross;  F2  and  F3  data  using  method  of  MLE  and other  methods;  Disturbed  segregation;  Estimation  of additive  genetic  dominance  and environmental components of variation; Plant Breeding trials and their use in the estimation of genetic variation and variability; Simple ideas  of discriminant function for plant selection. Path analysis; Genotypic correlation; Path coefficients. North – Carolina Mating Designs; NC Design I, II, III, Line X Tester design

 

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MATHEMATICAL METHODS - I  

Objective

•  
• This   course   lays   the   foundation   of   all   other   courses   of   Statistics/ Agricultural  Statistics  discipline  by  preparing  them  to  understand  the importance of mathematical methods in research.  differential equations and numerical analysis. This would prepare them to  study their main courses that involve knowledge of Mathematics.  

Theory 

• UNIT I
• Real  Analysis:  Convergence  and  divergence  of  infinite  series,  use  of  comparison   tests   -D'Alembert's   Ratio   -   test,   Cauchy's   nth   root   test,  Raabe's   test,   Kummer's   test,   Gauss   test.   Absolute   and   conditional  convergence. Riemann integration, concept of Lebesgue integration, power  series,  Fourier,  Laplace  and  Laplace  -Steiltjes'  transformation,  multiple  integrals. 
• UNIT II
• Calculus:  Limit  and  continuity,  differentiation  of  functions,  successive  differentiation,  partial  differentiation,  mean  value  theorems,  Taylor  and  Maclaurin's series. Application of derivatives, L'hospital's rule. Integration  of    rational,    irrational    and    trigonometric    functions.    Application    of  integration.  
• UNIT III
• Differential equation: Differential equations of first order, linear differential  equations of higher order with constant coefficient.  
• UNIT IV
• Numerical Analysis: Simple interpolation, Divided differences, Numerical  differentiation and integration.  

 

Suggested Readings 

• Bartle RG. 1976. Elements of Real Analysis. John Wiley.  
• Chatterjee SK. 1970. Mathematical Analysis. Oxford & IBH.  
• Gibson GA. 1954. Advanced Calculus. Macmillan.  
• Henrice P. 1964. Elements of Numerical Analysis. John Wiley.  
• Hildebrand  FB.  1956.  Introduction  to  Numerical  Analysis.  Tata  McGraw  Hill.  
• Priestley HA. 1985. Complex Analysis. Clarendon Press.  
• Rudin W. 1985. Principles of Mathematical Analysis. McGraw Hill.  Sauer T. 2006. Numerical Analysis With CD-Rom. Addison Wesley.  
• Scarborough JB. 1976. Numerical Mathematical Analysis. Oxford & IBH.  Stewart J. 2007. Calculus. Thompson.  
• Thomas GB Jr. & Finney RL. 1996. Calculus. 9^th Ed. Pearson Edu.  

 

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MATHEMATICAL METHODS - II  

Objective  

• This  is  another  course  that  supports  all  other  courses  in  Statistics  /  
• Agricultural Statistics. The students would be exposed to the advances in  Linear Algebra and Matrix theory. This would prepare them to study their  main  courses  that  involve  knowledge  of  Linear  Algebra  and  Matrix  Algebra.  

Theory 

• UNIT I
• Linear  Algebra:  Group,  ring,  field  and  vector  spaces,  Sub-spaces,  basis,  
• Gram  Schmidt's  orthogonalization,  Galois  field  -  Fermat's  theorem  and  
• primitive  elements.  Linear  transformations.  Graph  theory:  Concepts  and  applications  
• UNIT II
• Matrix Algebra: Basic terminology, linear independence and dependence of  vectors.  Row  and  column  spaces,  Echelon  form.  Determinants,  rank  and  inverse of matrices. Special matrices - idempotent, symmetric, orthogonal.  Eigen values and eigen vectors. Spectral decomposition of matrices  
• UNIT III
• Unitary, Similar, Hadamard, Circulant, Helmert's matrices. Kronecker and  Hadamard  product  of  matrices,  Kronecker  sum  of  matrices.  Sub-matrices  and  partitioned  matrices,  Permutation  matrices,  full  rank  factorization,  Grammian  root  of  a  symmetric  matrix.  Solutions  of  linear  equations,  Equations having many solutions.  
• UNIT IV
• Generalized  inverses,  Moore-Penrose  inverse,  Applications  of  g-inverse.  Spectral  decomposition  of  matrices,  Inverse  and  Generalized  inverse  of  partitioned matrices, Differentiation and integration of matrices, Quadratic  forms.  

 

Suggested Readings 

• Aschbacher M. 2000. Finite Group Theory. Cambridge University Press.  
• Deo   N.   1984.   Graph   Theory   with   Application   to   Engineering   and Computer Science. Prentice Hall of India.  
• Gentle JE. 2007. Matrix Algebra: Theory, Computations and Applications in Statistics. Springer.  
• Graybill FE.1961. Introduction to Matrices with Applications in Statistics.  Wadsworth Publ.  
• Hadley G. 1969. Linear Algebra. Addison Wesley.  
• Harville  DA.  1997.  Matrix  Algebra  from  a  Statistician's  Perspective.  
• Springer.  
• Rao  CR.  1965.   Linear  Statistical  Inference  and  its  Applications.  2  nd  Ed. John Wiley.  
• Robinson DJS. 1991. A Course in Linear Algebra with Applications. World  Scientific.  
• Searle SR. 1982. Matrix Algebra Useful for Statistics. John Wiley.  
• Seber GAF. 2008. A Matrix Handbook for Statisticians. John Wiley.  

 

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PROBABILITY THEORY 

Objective  

• This is a fundamental course in Statistics. This course lays the foundation  of     probability     theory,     random     variable,     probability     distribution,  mathematical expectation, etc. which forms the basis of basic statistics. The  students  are  also  exposed  to  law  of  large  numbers  and  central  limit  theorem. The students also get introduced to stochastic processes.  

Theory 

• UNIT I
• Basic  concepts  of  probability.  Elements  of  measure  theory:  class  of  sets,  field,  sigma  field,  minimal  sigma  field,  Borel  sigma  field  in  R,  measure,  probability  measure.  Axiomatic  approach  to  probability.    Properties  of  probability  based  on  axiomatic  definition.  Addition  and  multiplication  theorems.  Conditional  probability  and  independence  of  events. Bayes theorem.  
• UNIT II
• Random   variables: definition of random variable, discrete and continuous,  functions  of  random  variables.  Probability  mass  function  and  Probability  density   function,   Distribution   function   and   its   properties.   Notion   of  bivariate    random    variables,    bivariate    distribution    function    and    its  properties.   Joint,  marginal and conditional distributions. Independence of  random  variables.  Transformation  of  random  variables  (two  dimensional  case only).  
• Mathematical  expectation:    Mathematical  expectation  of  functions  of  a  random variable.   Raw and central moments and their relation, covariance,  skewness    and    kurtosis.    Addition    and    multiplication    theorems    of  expectation.      Definition   of   moment   generating   function,   cumulating  generating function, probability generating function and statements of their  properties.  
• UNIT III
• Conditional  expectation  and  conditional  variance.   Characteristic  function  and  its  properties.   Inversion  and  uniqueness  theorems.  Functions,  which  cannot be characteristic functions.  
• Chebyshev,  Markov,  Cauchy-Schwartz,  Jenson,  Liapounov,  holder's  and  Minkowsky's  inequalities.  Sequence  of  random  variables  and  modes  of  convergence (convergence in distribution, in probability, almost surely, and  quadratic  mean)  and  their  interrelations.  Statement  of  Slutsky's  theorem.  Borel -Cantelli lemma and Borel 0-1 law.  
• UNIT IV
• Laws   of   large   numbers:   WLLN,   Bernoulli   and   Kintchin's   WLLN.  
• Kolmogorov inequality, Kolmogorov's SLLNs.  
• Central Limit theorems:  Demoviere- Laplace CLT, Lindberg - Levy CLT,  Liapounov    CLT,    Statement    of    Lindeberg-Feller    CLT    and    simple  applications.    Definition    of    quantiles    and    statement    of    asymptotic  distribution of sample quantiles.  
• UNIT V
• Classification   of   Stochastic   Processes,   Examples.   Markov   Chain   and  classification of states of Markov Chain.  

 

Suggested Readings           

• Ash RB. 2000. Probability and Measure Theory. 2    Ed. Academic Press.  nd  
• Billingsley P. 1986. Probability and Measure. 2    Ed. John Wiley.  
• Capinski M & Zastawniah. 2001. Probability Through Problems. Springer.  
• Dudewicz  EJ  &  Mishra  SN.  1988.  Modern  Mathematical  Statistics.  John  Wiley.  
• Feller W. 1972. An Introduction to Probability Theory and its Applications.  Vols. I., II. John Wiley.  
• Loeve M. 1978. Probability Theory. 4 th        Ed. Springer.  
• Marek  F.  1963.  Probability  Theory  and  Mathematical  Statistics.  John  Wiley.  
• Rohatgi VK & Saleh AK Md. E. 2005. An Introduction to Probability and 
• Statistics. 2    Ed. John Wiley.  

 

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STATISTICAL METHODS 

Objective  

• This  course  lays  the  foundation  of  probability  distributions  and  sampling  distributions  and  their  application  which  forms  the  basis  of  Statistical  Inference.  Together  with  probability  theory,  this  course  is  fundamental  to  the discipline of Statistics. The students are also exposed to correlation and  regression,  and  order  statistics  and  their  distributions.  Categorical  data  analysis is also covered in this course.  

 

Theory 

• UNIT I
• Descriptive    statistics:    probability    distributions:    Discrete    probability  distributions ~ Bernoulli, Binomial, Poisson, Negative-binomial, Geometric  and   Hyper   Geometric,   uniform,   multinomial   ~   Properties   of   these  distributions and real life examples. Continuous probability distributions ~  rectangular,  exponential,  Cauchy,  normal,  gamma,  beta  of  two  kinds,  Weibull,   lognormal,   logistic,   Pareto.   Properties   of   these   distributions.  Probability distributions of functions of random variables.  
• UNIT II
• Concepts of compound, truncated and mixture distributions (definitions and  examples).  Pearsonian curves and its various types. Sampling distributions  of sample mean and sample variance from Normal population, central and  non-central  chi-Square,  t  and  F  distributions,  their  properties  and  inter  relationships.  
• UNIT III
• Concepts  of  random  vectors,  moments  and  their  distributions.  Bivariate  Normal  distribution  -  marginal  and  conditional  distributions.  Distribution  of   quadratic   forms.   Cochran   theorem.     Correlation,   rank   correlation,  correlation ratio and intra-class correlation. Regression analysis, partial and  multiple correlation and regression.  
• UNIT IV
• Sampling   distribution   of  correlation   coefficient,   regression   coefficient,  correlation   ratio,   intra   class   correlation   coefficient.   Categorical   data  analysis   -   loglinear   models,   Association   between   attributes.   Variance  Stabilizing Transformations.  
• UNIT V
• Order  statistics,  distribution  of  r-th  order  statistics,  joint  distribution  of  several order  statistics  and  their functions,  marginal  distributions  of  order  statistics, distribution of range, median, etc.  

 

Practical 

• Fitting  of  discrete  distributions  and  test  for  goodness  of    fit;  Fitting  of  continuous  distributions  and  test  for  goodness  of   fit;  Fitting  of  truncated  distribution;   Computation   of   simple,   multiple   and   partial   correlation  coefficient,    correlation    ratio    and    intra-class    correlation;    Regression  coefficients   and   regression   equations;   Fitting   of   Pearsonian   curves;  Analysis  of  association  between  attributes,  categorical  data  and  log-linear  models.  

 

Suggested Readings 

• Agresti A. 2002. Categorical Data Analysis. 2    Ed. John Wiley.  nd  
• Arnold  BC,  Balakrishnan  N  &  Nagaraja  HN.  1992.    A  First  Course  in Order Statistics. John Wiley.  
• David HA & Nagaraja HN. 2003. Order Statistics. 3   Ed. John Wiley.  rd 
• Dudewicz  EJ  &  Mishra  SN.  1988.  Modern  Mathematical  Statistics.  John  Wiley.  
• Huber PJ. 1981. Robust Statistics. John Wiley.  
• Johnson  NL,  Kotz  S  &  Balakrishnan  N.  2000.  Continuous  Univariate Distributions. John Wiley.  
• Johnson   NL,   Kotz   S   &   Balakrishnan   N.   2000.   Discrete   Univariate Distributions. John Wiley.  
• Marek    F.  1963.    Probability  Theory  and  Mathematical  Statistics.  John  Wiley.  
• Rao  CR.  1965.    Linear  Statistical  Inference  and  its  Applications.  John  Wiley.  
• Rohatgi VK & Saleh AK Md. E. 2005. An Introduction to Probability and 
• Statistics. 2    Ed. John Wiley.  

 

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STATISTICAL INFERENCE

Objective  

• This course lays the foundation of Statistical Inference. The students would  be taught the problems related to point and confidence interval estimation  and  testing  of  hypothesis.  They  would  also  be  given  the  concepts  of  nonparametric  and  sequential  test  procedures  and  elements  of  decision  theory.  Theory 
• UNIT I
• Concepts  of  point  estimation:  MSE,  unbiasedness,  consistency,  efficiency  and   sufficiency.   Statement   of   Neyman's   Factorization   theorem   with  applications.  MVUE,  Rao-Blackwell  theorem,  completeness,  Lehmann-  Scheffe  theorem.  Fisher  information,  Cramer-Rao  lower  bound  and  its  applications.  
• UNIT II
• Moments,  minimum  chi-square,  least  square  and  maximum  likelihood  methods of estimation and statements of their properties.     Interval  estimation-Confidence level, CI using pivots and shortest length CI. CI for  the parameters of Normal, Exponential, Binomial and Poisson distributions.  UNIT III
• Fundamental notions of hypothesis testing-statistical hypothesis, statistical  test,  critical  region,  types  of  errors,  test  function,  randomized  and  non-  randomized  tests,  level  of  significance,  power  function,  most  powerful  tests: Neyman-Pearson fundamental lemma, MLR families and UMP tests  for    one    parameter    exponential    families.    Concepts    of    consistency,  unbiasedness and invariance of tests.   Likelihood Ratio tests, statement of  asymptotic properties of LR tests with applications (including homogeneity  of  means  and  variances).Relation  between  confidence  interval  estimation  and testing of hypothesis.  
• UNIT IV
• Notions  of  sequential  vs  fixed  sample  size  techniques.  Wald's  SPRT  for  testing  simple null hypothesis vs simple alternative. Termination property   of   SPRT,   SPRT   for   Binomial,   Poisson,   Normal   and   Exponential  distributions.  Concepts of loss, risk and decision functions, admissible and  optimal  decision  functions,  estimation  and  testing  viewed  as  decision  problems, conjugate families, Bayes and Minimax decision functions with  applications to estimation with quadratic loss.  
• UNIT V
• Non-parametric  tests:  Sign  test,  Wilcoxon  signed  rank  test,  Runs  test  for  randomness,  Kolmogorov -  Smirnov  test for  goodness  of  fit,  Median test  and  Wilcoxon-Mann-Whitney  U-test.  Chi-square  test  for  goodness  of  fit  and  test  for  independence  of  attributes.   Kruskal  -Wallis  and  Friedman's  tests.    Spearman's    rank    correlation    and    Kendall's    Tau    tests    for  independence.  

 

Practical 

• Methods of estimation - Maximum Likelihood, Minimum χ   and Moments;  2 Confidence  Interval  Estimation;  MP  and  UMP  tests;  Large  Sample  tests;  Non-parametric    tests,    Sequential    Probability    Ratio    Test;    Decision  functions.  

 

Suggested Readings 

• Box  GEP  &  Tiao  GC.  1992.  Bayesian  Inference  in  Statistical  Analysis.  John Wiley.  
• Casela  G  &  Berger  RL.  2001.  Statistical  Inference.  Duxbury  Thompson  Learning.  
• Christensen R. 1990. Log Linear Models. Springer.  
• Conover WJ. 1980. Practical Nonparametric Statistics. John Wiley.  
• Dudewicz  EJ  &  Mishra  SN.  1988.  Modern  Mathematical  Statistics.  John Wiley.  
• Gibbons  JD.  1985.  Non  Parametric  Statistical  Inference.  2  nd  Ed.  Marcel  Dekker.  
• Kiefer JC. 1987. Introduction to Statistical Inference. Springer.  
• Lehmann EL. 1986. Testing Statistical Hypotheses. John Wiley.  
• Lehmann EL. 1986. Theory of Point Estimation. John Wiley.  
• Randles   RH   &   Wolfe   DS.   1979.   Introduction   to   the   Theory   of Nonparametric Statistics. John Wiley. 
• Rao  CR.  1973.   Linear  Statistical  Inference  and  its  Applications.  2  nd  Ed. John Wiley.  
• Rohatgi VK & Saleh AK. Md. E. 2005. An Introduction to Probability and Statistics. 2    Ed. John Wiley.  
• Rohtagi VK. 1984. Statistical Inference. John Wiley  
• Sidney S & Castellan NJ Jr. 1988. Non Parametric Statistical Methods for Behavioral Sciences. McGraw Hill.  
• Wald A. 2004. Sequential Analysis. Dover Publ.  

 

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MULTIVARIATE ANALYSIS  

Objective  

• This course lays the foundation of Multivariate data analysis. Most of the  data  sets  in  agricultural  sciences  are  multivariate  in  nature.  The  exposure  provided   to   multivariate   data   structure,   multinomial   and   multivariate  normal  distribution,  estimation  and  testing  of  parameters,  various  data  reduction methods would help the students in having a better understanding  of agricultural research data, its presentation and analysis.  

Theory 

• UNIT I
• Concept of random vector, its expectation and Variance-Covariance matrix.  
• Marginal    and    joint    distributions.        Conditional    distributions    and  
• Independence  of  random  vectors.   Multinomial  distribution.   Multivariate  Normal distribution, marginal and conditional distributions.   Sample mean  vector and  its distribution.  Maximum likelihood estimates  of mean vector  and dispersion matrix. Tests of hypothesis about mean vector.  
• UNIT II
• Wishart   distribution   and   its   simple   properties.
• Mahalanobis  D   statistics.  Null  distribution  of  Hotelling's  T .    Rao's  U  2        Hotelling's   T    and 2  statistics and its distribution.  
• Wilks' λ criterion and statement of its properties. Concepts of discriminant  analysis,   computation   of   linear   discriminant   function,   classification  between  k  (  ≥2)  multivariate  normal  populations  based  on  LDF  and  Mahalanobis D .  
• UNIT III
• Principal  Component  Analysis,  factor  analysis  (simple  and  multi  factor  models).   Canonical variables and canonical correlations. Cluster analysis,  similarities    and    dissimilarities,    Hierarchical    clustering.    Single    and  Complete linkage methods.  
• UNIT IV
• Path   analysis   and   computation   of   path   coefficients,   introduction   to  multidimensional scaling, some theoretical results, similarities, metric and  non metric scaling methods.  Concepts of analysis of categorical data.  

 

Practical 

• Maximum  likelihood   estimates  of   mean-vector  and  dispersion   matrix;  
• Testing of hypothesis on mean vectors of multivariate normal populations;  Cluster  analysis,  Discriminant  function,  Canonical  correlation,  Principal  component analysis, Factor analysis; Multivariate analysis of variance and  covariance, multidimensional scaling.  

 

Suggested Readings 

• Anderson TW. 1984.   An Introduction to Multivariate Statistical Analysis.  2    Ed. John Wiley.  
• Arnold SF. 1981. The Theory of Linear Models and Multivariate Analysis.  John Wiley.  
• Giri NC. 1977. Multivariate Statistical Inference. Academic Press.  
• Johnson   RA   &   Wichern   DW.   1988.   Applied   Multivariate   Statistical Analysis. Prentice Hall.  
• Kshirsagar AM. 1972.  Multivariate Analysis. Marcel Dekker.  
• Muirhead RJ. 1982. Aspects of Multivariate Statistical Theory. John Wiley.            nd  Ed.  
• Rao  CR.  1973.   Linear  Statistical  Inference  and  its  Applications.  2 John Wiley. 
• Rencher AC. 2002. Methods of Multivariate Analysis. 2nd Ed. John Wiley.  
• Srivastava   MS   &   Khatri   CG.   1979.   An   Introduction   to   Multivariate Statistics. North Holland.  

 

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DESIGN OF EXPERIMENTS

Objective  

• Design  of  Experiments  provides  the  statistical  tools  to  get  maximum  information from least amount of resources.  This course is meant to expose  the students to the basic principles of design of experiments. The students  would  also  be  provided  with a mathematical  background  of  various  basic  designs  involving one-way  and two way  elimination of heterogeneity  and  their   characterization   properties.   This   course   would   also   prepare   the  students in deriving the expressions for analysis of experimental data.  

 

Theory 

• UNIT I
• Elements   of   linear   estimation,   Gauss   Markoff   Theorem,   relationship  between BLUEs and linear zero-functions. Aitken's transformation, test of  hypothesis, analysis of variance, partitioning of degrees of freedom.  
• UNIT II
• Orthogonality,   contrasts,   mutually   orthogonal   contrasts,   analysis   of  covariance;  Basic  principles  of  design  of  experiments,  uniformity  trials,  size and shape of plots and blocks.  
• UNIT III
• Basic designs - completely randomized design, randomized complete block  design   and   Latin   square   design;   orthogonal   Latin   squares,   mutually  orthogonal  Latin  squares  (MOLS),  Youden  square  designs,  Graeco  Latin  squares.  
• UNIT IV
• Balanced incomplete block (BIB) designs - general properties and analysis  without and with recovery of intra block information, construction of BIB  designs.  Partially  balanced  incomplete block  designs  with  two  associate  classes   -   properties,   analysis   and   construction,   Lattice   designs,   alpha  designs,  cyclic  designs,  augmented  designs,  general  analysis  of  block  designs.  
• UNIT V
• Factorial  experiments,  confounding  in symmetrical  factorial  experiments  (2  and   3    series),   partial   and   total   confounding,   fractional   factorials,  n                n  asymmetrical factorials. 
• UNIT VI
• Designs  for  fitting  response  surface;  Cross-over  designs.  Missing  plot  technique;   Split   plot   and   Strip   plot   design;   Groups   of   experiments;  Sampling in field experiments.  

 

Practical 

• Determination of size and shape of plots and blocks from uniformity trials  data;  Analysis  of  data  generated  from  completely  randomized  design,  randomized  complete  block  design;  Latin  square  design,  Youden  square  design; Analysis of data generated from a BIB design, lattice design, PBIB  designs;  2 ,  3   factorial  experiments  without  and  with  confounding;  Split  n      n  and   strip   plot   designs,   repeated   measurement   design;   Missing   plot  techniques,  Analysis  of  covariance;  Analysis  of  Groups  of  experiments,  Analysis of clinical trial experiments. Sampling in field experiments.  

 

Suggested Readings  

• Chakrabarti    MC.    1962.    Mathematics    of    Design    and    Analysis    of Experiments. Asia Publ. House. 
• Cochran WG & Cox DR. 1957. Experimental Designs. 2    Ed. John Wiley. nd       Dean AM & Voss D. 1999. Design and Analysis of Experiments. Springer. 
• Dey A & Mukerjee R. 1999. Fractional Factorial Plans. John Wiley. 
• Dey A 1986. Theory of Block Designs. Wiley Eastern. 
• Hall M Jr. 1986. Combinatorial Theory. John Wiley. 
• John  JA  &  Quenouille  MH.  1977.  Experiments:  Design  and  Analysis. Charles & Griffin. 
• Kempthorne, O. 1976. Design and Analysis of Experiments. John Wiley. 
• Khuri AI & Cornell JA. 1996. Response Surface Designs and Analysis. 2   nd  Ed. Marcel Dekker. 
• Kshirsagar AM 1983.  A Course in Linear Models. Marcel Dekker. 
• Montgomery DC. 2005. Design and Analysis of Experiments. John Wiley. 
• Raghavarao D. 1971. Construction and Combinatorial Problems in Design of Experiments. John Wiley. 
• Searle SR. 1971.  Linear Models. John Wiley. 
• Street  AP  &  Street  DJ.  1987.  Combinatorics  of  Experimental  Designs. Oxford Science Publ. 
• Design    Resources    Server.    Indian    Agricultural    Statistics    Research Institute(ICAR), New Delhi-110012, India. www.iasri.res.in/design. 

 

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SAMPLING TECHNIQUES

Objective  

• This  course  is  meant  to  expose  the  students  to  the  techniques  of  drawing  representative  samples  from  various  populations  and  then  preparing  them  on the mathematical formulations of estimating the population parameters  based on the sample data. The students would also be exposed to the real  life applications of sampling techniques and estimation of parameters.  

 

Theory 

• UNIT I
• Sample  survey  vs  complete  survey,  probability  sampling,  sample  space,  sampling  design,  sampling  strategy;  Inverse  sampling;   Determination  of  sample size; Confidence-interval; Simple random sampling,   Estimation of  population  proportion,  Stratified  random  sampling,  Number  of  strata  and  optimum points of stratification.  
• UNIT II
• Ratio  and regression  methods of estimation, Cluster sampling, Systematic  sampling,   Multistage   sampling   with   equal   probability,   Separate   and  combined  ratio  estimator,    Double  sampling,  Successive  sampling  -two  occasions. 
• UNIT III
• Non-sampling errors - sources and classification, Non-response in surveys,  Imputation  methods,  Randomized  response  techniques,  Response  errors  -  interpenetrating sub-sampling.  
• UNIT IV
• Sampling  with  varying  probabilities  with  and  without  replacement,  PPS  sampling,  Cumulative  method  and  Lahiri's  method  of  selection,  Horvitz-  Thompson    estimator,    Ordered    and    unordered    estimators,    Sampling  strategies   due   to   Midzuno-Sen   and   Rao-Hartley-Cochran.   Inclusion  probability   proportional   to   size   sampling,   PPS   systematic   sampling,  Multistage sampling with unequal probabilities, Self weighting design PPS  sampling.  
• UNIT V
• Unbiased   ratio   and   regression   type   estimators,   Multivariate   ratio   and  regression   type   of   estimators,   Design   effect,   Bernoulli   and   Poisson  sampling.  

 

Practical 

• Determination  of  sample  size  and  selection  of  sample;  Simple  random  sampling, Inverse sampling, Stratified random  sampling, Cluster sampling,  systematic  sampling;  Ratio  and regression  methods  of  estimation;  Double  sampling,    multi-stage    sampling,    Imputation    methods;    Randomized  response techniques; Sampling with varying probabilities.  

 

Suggested Readings 

• Cassel CM, Sarndal CE & Wretman JH. 1977. Foundations of Inference in Survey Sampling. John Wiley.  
• Chaudhari A & Stenger H. 2005. Survey Sampling Theory and Methods. 2            nd  Ed. Chapman & Hall.  
• Chaudhari A & Voss JWE. 1988. Unified Theory and Strategies of Survey Sampling. North Holland.  
• Cochran WG. 1977. Sampling Techniques. John Wiley.  
• Hedayat AS & Sinha BK. 1991. Design and Inference in Finite Population Sampling. John Wiley.  
• Kish L. 1965. Survey Sampling. John Wiley.  
• Murthy MN. 1977. Sampling Theory and Methods. 2    Ed. Statistical Publ.  nd  Society, Calcutta.  
• Raj D &  Chandhok P. 1998. Sample Survey Theory. Narosa Publ.  
• Sarndal  CE,  Swensson  B  &  Wretman  J.  1992.  Models    Assisted  Survey Sampling. Springer.  
• Sukhatme  PV,  Sukhatme  BV,  Sukhatme  S  &  Asok  C.  1984.  Sampling Theory  of  Surveys  with  Applications.  Iowa  State  University  Press  and Indian Society of Agricultural Statistics, New Delhi.  Thompson SK. 2000. Sampling. John Wiley.  

 

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STATISTICAL GENETICS

Objective  

• This course is meant to prepare the students in applications of statistics in  quantitative  genetics  and  breeding.  The  students  would  be  exposed  to  the  physical   basis   of   inheritance,   detection   and   estimation   of   linkage,  estimation of genetic parameters and development of selection indices.  

Theory 

• UNIT I
• Physical   basis   of   inheritance.   Analysis   of   segregation,   detection   and  estimation  of  linkage  for  qualitative  characters.  Amount  of  information  about linkage, combined estimation, disturbed segregation.  
• UNIT II
• Gene  and  genotypic  frequencies,  Random  mating  and  Hardy  -Weinberg  law,    Application    and    extension    of    the    equilibrium    law,    Fisher's  fundamental theorem of natural selection. Disequilibrium due to linkage for  two pairs of genes, sex-linked genes, Theory of path coefficients.  
• UNIT III
• Concepts  of  inbreeding,  Regular  system  of  inbreeding.  Forces  affecting  gene  frequency  -  selection,  mutation  and  migration,  equilibrium  between  forces   in   large   populations,   Random   genetic   drift,   Effect   of   finite  population size.  
• UNIT IV
• Polygenic  system  for  quantitative  characters,  concepts  of  breeding  value  and  dominance  deviation.  Genetic  variance  and  its  partitioning,  Effect  of  inbreeding   on   quantitative   characters,   Multiple   allelism   in   continuous  variation,   Sex-linked   genes,   Maternal   effects   -   estimation   of   their  contribution. 
• UNIT V
• Correlations   between   relatives,   Heritability,   Repeatability   and   Genetic  correlation. Response due to selection, Selection index and its applications  in  plants  and  animals  improvement  programmes,  Correlated  response  to  selection.  UNIT VI
• Restricted   selection   index.   Variance   component   approach   and   linear  regression  approach  for  the  analysis  of  GE  interactions.  Measurement  of  stability  and  adaptability  for  genotypes.  Concepts  of  general  and  specific  combining  ability.  Diallel  and  partial  diallel  crosses  -  construction  and  analysis.  

 

Practical 

• Test  for  the  single  factor  segregation  ratios,  homogeneity  of  the  families  with  regard  to  single  factor  segregation;  Detection  and  estimation  of  linkage  parameter  by  different  procedures;  Estimation  of  genotypic  and  gene  frequency  from  a  given  data.  Hardy-Weinberg  law;  Estimation  of  changes in gene frequency due to systematic forces, inbreeding coefficient,  genetic  components  of  variation,  heritability  and  repeatability  coefficient,  genetic  correlation  coefficient;  Examination  of  effect  of  linkage,  epistasis  and  inbreeding  on  mean  and  variance  of  metric  traits;  Mating  designs;  Construction   of   selection   index   including   phenotypic  index,   restricted  selection index. Correlated response to selection.  

 

Suggested Readings 

• Bailey   NTJ.   1961.   The   Mathematical   Theory   of   Genetic   Linkage.  Clarendon Press.  
• Balding  DJ,  Bishop  M  &  Cannings  C.  2001.  Hand  Book  of  Statistical Genetics. John Wiley.  
• Crow  JF  &  Kimura  M.  1970.  An  Introduction  of  Population  Genetics Theory. Harper & Row.  
• Dahlberg  G.  1948.  Mathematical  Methods  for  Population  Genetics.  Inter  Science Publ.  
• East EM & Jones DF. 1919. Inbreeding and Outbreeding.  J B Lippincott.  
• Ewens WJ. 1979. Mathematics of Population Genetics. Springer.  
• Falconer DS. 1985. Introduction to Quantitative Genetics. ELBL.  
• Fisher RA. 1949. The Theory of Inbreeding.  Oliver & Boyd.  
• Fisher  RA.  1950.  Statistical  Methods  for  Research  Workers.  Oliver  &  Boyd.  
• Fisher RA. 1958. The Genetical Theory of Natural Selection. Dover Publ.  
• Kempthorne O. 1957. An Introduction to Genetic Statistics. The Iowa State  Univ. Press.  
• Lerner    IM.    1950.    Population    Genetics    and    Animal    Improvement.  Cambridge Univ. Press.  
• Lerner IM. 1954. Genetic Homeostasis. Oliver & Boyd.  
• Lerner IM. 1958. The Genetic Theory of Selection. John Wiley.  
• Li CC. 1982. Population Genetics. The University of Chicago Press.  
• Mather   K   &   Jinks   JL.   1977.   Introduction   to   Biometrical   Genetics.  Chapman & Hall.  
• Mather K & Jinks JL. 1982. Biometrical Genetics. Chapman & Hall.  
• Mather K. 1949. Biometrical Genetics. Methuen.  
• Mather K. 1951.  The Measurement of Linkage in Heredity. Methuen.  Narain P. 1990. Statistical Genetics. Wiley Eastern.  

 

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REGRESSION ANALYSIS 

Objective  

• This  course  is  meant  to  prepare  the  students  in  linear  and  non-linear  regression methods useful for statistical data analysis. They would also be  provided  a  mathematical  foundation  behind  these  techniques  and  their  applications in agricultural data.  

Theory 

• UNIT I
• Simple  and  Multiple  linear  regressions:  Least  squares  fit,  Properties  and  examples. Polynomial regression: Use of orthogonal polynomials.  
• UNIT II
• Assumptions  of  regression;  diagnostics  and  transformations;  Examination  of  residuals  ~  Studentized residuals,  applications  of  residuals  in detecting  outliers,  identification  of  influential  observations.  Lack  of  fit,  Pure  error.  Testing homoscedasticity and normality of errors, Durbin-Watson test. Use of R  for examining goodness of fit.  
• UNIT III
• Concepts  of  Least  median  of  squares  and  its  applications;  Concept  of  multicollinearity,  Analysis  of  multiple  regression  models,  estimation  and  testing    of    regression    parameters,    sub-hypothesis    testing,    restricted  estimation.  
• UNIT IV
• Weighted least squares method: Properties, and examples. Box-Cox family  of   transformations.   Use   of   dummy   variables,   Selection   of   variables:  Forward    selection,    Backward    elimination.    Stepwise    and    Stagewise  regressions.  
• UNIT V
• Introduction  to non-linear  models,  nonlinear  estimation: Least squares  for  nonlinear models.  

 

Practical  

• Multiple  regression  fitting  with  three  and  four  independent  variables; Estimation of residuals,  their applications in outlier  detection,  distribution of   residuals;   Test   of    homoscedasticity,   and   normality,       Box-Cox transformation;    Restricted    estimation    of    parameters    in    the    model, hypothesis testing, Step wise regression analysis; Least median of squares norm, Orthogonal polynomial fitting. 

 

Suggested Readings  

• Barnett V & Lewis T. 1984. Outliers in Statistical Data. John Wiley. 
• Belsley   DA,   Kuh   E   &   Welsch   RE.   2004.   Regression   Diagnostics- Identifying   Influential   Data   and   Sources   of   Collinearity.   John Wiley. 
• Chatterjee S, Hadi A & Price B. 1999. Regression Analysis by Examples. John Wiley. 
• Draper  NR  &  Smith  H.  1998.  Applied  Regression  Analysis.  3    Ed.  John rd Wiley. 
• McCullagh  P  &  Nelder  JA.  1999.  Generalized  Linear  Models.  2  nd  Ed. Chapman & Hall.  
• Montgomery  DC,  Peck  EA  &  Vining  GG.  2003.  Introduction  to  Linear 
• Regression Analysis. 3   Ed. John Wiley. rd
• Rao  CR.  1973.   Linear  Statistical  Inference  and  its  Applications.  2  nd  Ed. John Wiley.  

 

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STATISTICAL COMPUTING

Objective  

• This   course   is   meant   for   exposing   the   students   in   the   concepts   of  computational techniques. Various statistical packages would be used for  teaching the concepts of computational techniques.  

 

Theory 

• UNIT I
• Introduction   to   statistical   packages   and   computing:   data   types   and  structures,  pattern  recognition,  classification,  association  rules,  graphical  methods.  Data analysis principles and practice  UNIT II
• ANOVA,  regression  and  categorical  data  methods;  model  formulation,  fitting,  diagnostics  and  validation;  Matrix  computations  in  linear  models.  Analysis of discrete data.  
• UNIT III
• Numerical  linear  algebra,  numerical  optimization,  graphical  techniques,  numerical    approximations,    numerical    integration    and    Monte    Carlo  methods.  
• UNIT IV
• Spatial   statistics;   spatial   sampling;   hierarchical   modeling.   Analysis   of  cohort   studies,   case-control   studies   and   randomized   clinical   trials,  techniques   in   the   analysis   of   survival   data   and   longitudinal   studies,  Approaches to handling missing data, and meta-analysis.  

 

Practical 

• Data management, Graphical representation of data, Descriptive statistics;  
• General linear models ~ fitting and analysis of residuals, outlier detection;  
• Categorical data analysis, analysis of discrete data, analysis of binary data;  Numerical  algorithms;  Spatial  modeling,  cohort  studies;  Clinical  trials,  analysis of survival data; Handling missing data.  

 

Suggested Readings  

• Agresti A. 2002. Categorical Data Analysis. 2    Ed. John Wiley.  nd  
• Everitt BS & Dunn G. 1991. Advanced Multivariate Data Analysis. 2    Ed.  nd  Arnold.  
• Geisser S. 1993. Predictive Inference: An Introduction. Chapman & Hall.  
• Gelman   A   &   Hill   J.   2006.   Data   Analysis   Using   Regression   and Multilevel/Hierarchical Models. Cambridge Univ. Press.  
• Gentle  JE,  Härdle  W  &  Mori  Y.  2004.  Handbook  of  Computational Statistics - Concepts and Methods. Springer.  
• Han  J  &  Kamber  M.  2000.  Data  Mining:  Concepts  and  Techniques.  Morgan.  
• Hastie  T,  Tibshirani  R  &  Friedman  R.  2001.  The  Elements  of  Statistical Learning: Data Mining, Inference and Prediction. Springer.  
• Kennedy WJ & Gentle JE. 1980. Statistical Computing. Marcel Dekker.  
• Miller  RG  Jr.  1986.  Beyond  ANOVA,  Basics  of  Applied  Statistics.  John  Wiley.  
• Rajaraman V. 1993. Computer Oriented Numerical Methods. Prentice-Hall.  
• Ross S. 2000. Introduction to Probability Models. Academic Press.  
• Ryan BF & Joiner BL. 1994. MINITAB Handbook. 3   Ed. Duxbury Press.  
• Simonoff JS. 1996. Smoothing Methods in Statistics. Springer.  
• Snell   EJ.   1987.   Applied   Statistics:   A   Handbook   of   BMDP   Analyses.  Chapman & Hall.  
• Thisted RA. 1988. Elements of Statistical Computing. Chapman & Hall.  
• Venables WN & Ripley BD. 1999. Modern Applied Statistics With S-Plus.  3   Ed. Springer.  

 

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TIME SERIES ANALYSIS 

Objective  

• This  course  is  meant  to  teach  the  students  the  concepts  involved  in  time  series  data.  They  would  also  be  exposed  to  components  of  time  series,  stationary models and forecasting/ projecting the future scenarios based on  time  series  data.   It  would  also  help  them  in  understanding  the  concepts  involved in time series data presentation, analysis and interpretation.  

 

Theory 

• UNIT I
• Components  of  a  time-series.  Autocorrelation  and  Partial  autocorrelation  functions, Correlogram and periodogram analysis.  
• UNIT II
• Linear  stationary  models:  Autoregressive,  Moving  average  and  Mixed  processes. Linear non-stationary models: Autoregressive integrated moving  average processes.  
• UNIT III
• Forecasting:   Minimum   mean   square   forecasts   and   their   properties,  Calculating and updating forecasts.  
• UNIT IV
• Model identification: Objectives, Techniques, and Initial estimates. Model  estimation:  Likelihood  function,  Sum  of  squares  function,  Least  squares  estimates.   Seasonal   models.   Intervention   analysis   models   and   Outlier  detection.  

 

Practical 

• Time   series   analysis,   autocorrelations,   correlogram   and   periodogram;  Linear stationary model; Linear non-stationary model; Model identification  and model estimation; Intervention analysis and outliers detection.  
• Suggested Readings 
• Box   GEP,   Jenkins   GM   &   Reinsel   GC.   2007.   Time   Series   Analysis: rd Forecasting and Control. 3   Ed. Pearson Edu.  
• Brockwell   PJ   &   Davis   RA.   2002.   Introduction   to   Time   Series   and nd Forecasting. 2    Ed. Springer.  
• Chatterjee  S,  Hadi  A  &  Price  B.1999.  Regression  Analysis  by  Examples.     John Wiley.     rd 
• Draper  NR  &  Smith  H.  1998.  Applied  Regression  Analysis.  3    Ed.  John  Wiley.  
• Johnston J. 1984. Econometric Methods. McGraw Hill.  
• Judge   GG,   Hill   RC,   Griffiths   WE,   Lutkepohl   H   &   Lee   TC.   1988.  nd  Ed.  Introduction  to  the  Theory  and  Practice  of  Econometrics.  2 John Wiley. Montgomery  DC  &  Johnson  LA.  1976.  Forecasting  and  Time  Series Analysis. McGraw Hill.  
• Shumway   RH   &   Stoffer   DS.   2006.   Time   Series   Analysis   and   its Applications: With R Examples. 2    Ed. Springer.  

 

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ACTUARIAL STATISTICS

Objective  

• This course is meant to expose to the students to the statistical techniques  such   as   probability   models,   life   tables,   insurance   and   annuities.   The  students   would   also   be   exposed   top   practical   applications   of   these  techniques  in  computation  of  premiums  that  include  expenses,  general  expenses, types of expenses and per policy expenses.  

 

Theory 

• UNIT I
• Insurance  and utility  theory,  models for individual  claims  and their sums,  survival function, curtate future lifetime, force of mortality.  UNIT II
• Life table and its relation with survival function, examples, assumptions for  fractional  ages,  some  analytical  laws  of  mortality,  select  and  ultimate  tables.  
• UNIT III
• Multiple  life  functions,  joint  life  and  last  survivor  status,  insurance  and  annuity  benefits  through  multiple  life  functions  evaluation  for  special  mortality   laws.  Multiple  decrement   models,  deterministic  and  random  survivorship  groups,  associated  single  decrement  tables,  central  rates  of  multiple decrement, net single premiums and their numerical evaluations.  
• UNIT IV
• Distribution  of  aggregate  claims,  compound  Poisson  distribution  and  its  applications.  
• UNIT V
• Principles of compound interest: Nominal and effective rates of interest and  discount,  force  of  interest  and  discount,  compound  interest,  accumulation  factor, continuous compounding.  
• UNIT VI
• Insurance  payable  at  the  moment  of  death  and  at  the  end  of  the  year  of  death-level benefit insurance, endowment insurance, deferred insurance and  varying benefit insurance, recursions, commutation functions.  
• UNIT VII
• Life  annuities:  Single  payment,  continuous  life  annuities,  discrete  life  annuities,  life  annuities  with  monthly  payments,  commutation  functions,  varying     annuities,     recursions,     complete     annuities-immediate     and  apportionable annuities-due.  
• UNIT VIII
• Net  premiums:  Continuous  and  discrete  premiums,  true  monthly  payment  premiums, apportionable premiums, commutation functions, accumulation  type  benefits.  Payment  premiums,  apportionable  premiums,  commutation  functions,  accumulation  type  benefits.  Net  premium  reserves:  Continuous  and  discrete  net  premium  reserve,  reserves  on  a  semi-continuous  basis,  reserves based on true monthly premiums, reserves on an apportionable or  discounted continuous basis, reserves at fractional durations, allocations of  loss  to  policy  years,  recursive  formulas  and  differential  equations  for  reserves, commutation functions.  
• UNIT IX
• Some  practical  considerations:  Premiums  that  include  expenses-general  expenses    types    of    expenses,    per    policy    expenses.    Claim    amount  distributions, approximating the individual model, stop-loss insurance.  

 

Suggested Readings 

• Atkinson ME & Dickson DCM. 2000. An Introduction to Actuarial Studies.  Elgar Publ.  
• Bedford T & Cooke R. 2001. Probabilistic Risk Analysis. Cambridge.  
• Booth  PM,  Chadburn  RG,  Cooper  DR,  Haberman  S  &  James  DE.  1999.  
• Modern Actuarial Theory and Practice. Chapman & Hall.  
• Borowiak    Dale    S.    2003.    Financial    and    Actuarial    Statistics:    An Introduction. 2003. Marcel Dekker.  
• Bowers  NL,  Gerber  HU,  Hickman  JC,  Jones  DA  &  Nesbitt  CJ.  1997.  nd Actuarial Mathematics. 2    Ed. Society of Actuaries, Ithaca, Illinois.  
• Daykin CD, Pentikainen T & Pesonen M. 1994. Practical Risk Theory for Actuaries. Chapman & Hall.  
• Klugman  SA,  Panjer  HH,  Willmotand  GE  &  Venter  GG.  1998.  Loss Models: From data to Decisions. John Wiley.  
• Medina PK & Merino S. 2003. Mathematical Finance and Probability: A Discrete Introduction. Basel, Birkhauser.  
• Neill A. 1977. Life Contingencies. Butterworth-Heinemann.  
• Rolski T, Schmidli H, Schmidt V & Teugels J. 1998. Stochastic Processes for Insurance and Finance. John Wiley.  
• Rotar   VI.   2006.   Actuarial   Models.   The   Mathematics   of   Insurance.  Chapman & Hall/CRC.  
• Spurgeon ET. 1972. Life Contingencies. Cambridge Univ. Press.  

 

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BIOINFORMATICS

Objective  

• Bioinformatics  is  a   new  emerging  area.  It  is  an  integration  of  Statistics,  Computer applications and Biology.    The trained manpower in the area of  Bioinformatics is required for meeting the new challenges in teaching and  research in the discipline of Agricultural Sciences. This course is meant to  train  the  students  on  concepts  of  basic  biology,  statistical  techniques  and  computational techniques for understanding bioinformatics principals.  

 

Theory 

• UNIT I
• Basic Biology: Cell, genes, gene structures, gene expression and regulation,  Molecular tools, nucleotides, nucleic acids, markers, proteins and enzymes,  bioenergetics,  single  nucleotide  polymorphism,  expressed  sequence  tag.  Structural and functional genomics: Organization and structure of genomes,  genome  mapping,  assembling  of  physical  maps,  strategies  and  techniques  for genome sequencing and analysis.  
• UNIT II
• Computing  techniques:  OS  and  Programming  Languages  -  Linux,  perl,  bioperl,   cgi,   MySQL,   phpMyAdmin;   Coding   for   browsing   biological  databases  on  web,  parsing  &  annotation  of  genomic  sequences;  Database  designing; Computer networks - Internet, World wide web, Web browsers  - EMBnet, NCBI; Databases on public domain pertaining to Nucleic acid  sequences,  protein  sequences,  SNPs,  etc.;  Searching  sequence  databases,  Structural databases.  
• UNIT III
• Statistical Techniques: MANOVA, Cluster analysis, Discriminant analysis,  
• Principal      component      analysis,      Principal      coordinate      analysis,  Multidimensional    scaling;    Multiple    regression    analysis;    Likelihood  approach in estimation and testing; Resampling techniques - Bootstrapping  and Jack-knifing; Hidden Markov Models; Bayesian estimation and Gibbs  sampling;  
• UNIT IV
• Tools  for  Bioinformatics:  DNA  Sequence  Analysis  -  Features  of  DNA  sequence   analysis,   Approaches   to   EST   analysis;   Pairwise   alignment  techniques:   Comparing   two   sequences,   PAM   and   BLOSUM,   Global  alignment (The Needleman and Wunsch algorithm), Local Alignment (The  Smith-Waterman  algorithm),  Dynamic  programming,  Pairwise  database  searching;  Sequence  analysis-  BLAST  and  other  related  tools,  Multiple  alignment and  database  search using  motif  models,  ClustalW,  Phylogeny;  Databases on SNPs; EM algorithm and other methods to discover common  motifs   in   biosequences;   Gene   prediction   based   on   Neural   Networks,  Genetic  algorithms,  Hidden  Markov  models.  Computational  analysis  of  protein   sequence,   structure   and   function;   Design   and   Analysis   of  microarray experiments.  

 

Suggested Readings 

• Baldi   P   &   Brunak   S.   2001.   Bioinformatics:   The   Machine   Learning nd Approach. 2    Ed. (Adaptive Computation and Machine Learning).  MIT Press.  
• Baxevanis  AD  &  Francis  BF.  (Eds.).  2004.  Bioinformatics:  A  Practical Guide to the Analysis of Genes and Proteins. John Wiley.  
• Bergeron BP. 2002. Bioinformatics Computing. Prentice Hall.  
• Duda RO, Hart PE & Stork DG. 1999. Pattern Classification. John Wiley.  
• Ewens  WJ  &  Grant  GR.  2001.  Statistical  Methods  in  Bioinformatics:  An Introduction (Statistics for Biology and Health). Springer.  
• Hunt S & Livesy F. (Eds.). 2000. Functional Genomics: A Practical Approach (The Practical Approach Series, 235). Oxford Univ.  Press.  
• Jones   NC   &   Pevzner   PA.   2004.   An   Introduction   to   Bioinformatics Algorithims. MIT Press.  
• Koski T & Koskinen T. 2001. Hidden Markov Models for Bioinformatics.  Kluwer.  
• Krane DE & Raymer ML. 2002. Fundamental Concepts of Bio-informatics.  Benjamin / Cummings.  
• Krawetz  SA  &  Womble  DD.  2003.  Introduction  to  Bioinformatics:  A Theoretical and Practical Approach. Humana Press.  
• Lesk AM. 2002. Introduction to Bio-informatics. Oxford Univ. Press.  
• Percus  JK.  2001.  Mathematics  of  Genome  Analysis.  Cambridge  Univ.  Press.  
• Sorensen   D   &   Gianola   D.   2002.  Likelihood,   Bayesian   and   MCMC  Methods in Genetics. Springer.  
• Tisdall   JD.   2001.   Mastering   Perl   for   Bioinformatics.   O'Reilly   &  Associates.  
• Tisdall   JD.   2003.   Beginning   Perl   for   Bioinformatics.   O'Reilly   &  Associates.  
• Wang  JTL,  Zaki  MJ,  Toivonen  HTT  &  Shasha  D.  2004.  Data  Mining  in Bioinformatics. Springer.  
• Wu CH & McLarty JW. 2000. Neural Networks and Genome Informatics.  Elsevier.  
• Wunschiers R. 2004. Computational Biology Unix/Linux, Data Processing and Programming. Springer.  

 

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ECONOMETRICS

Objective  

• This course is meant for training the students in econometric methods and  their applications in agriculture. This course would enable the students in  understanding   the   economic   phenomena   through   statistical   tools   and  economics principles.  
• Theory 
• UNIT I
• Representation  of  Economic  phenomenon,  relationship  among  economic  variables,  linear and non linear  economic  models, single  equation general  linear regression model, basic assumptions, Ordinary least squares method  of estimation for simple and multiple regression models; summary statistics  correlation matrix, co-efficient of multiple determination, standard errors of  estimated   parameters,   tests   of   significance   and   confidence   interval  estimation. BLUE properties of Least Squares estimates. Chow test, test of  improvement  of  fit  through  additional  regressors.  Maximum  likelihood  estimation.  
• UNIT II
• Heteroscedasticity, Auto-correlation, Durbin Watson test, Multicollinearity.  
• Stochastic regressors,  
• Errors  in  variables,  Use  of  instrumental  variables  in  regression  analysis.  Dummy   Variables.   Distributed   Lag   models:   Koyck's   Geometric   Lag  scheme,  Adaptive  Expectation  and  Partial  Adjustment  Mode,  Rational  Expectation Models and test for rationality.  
• UNIT III
• Simultaneous    equation    model:    Basic    rationale,    Consequences    of  simultaneous relations, Identification problem, Conditions of Identification,  Indirect   Least   Squares,   Two-stage   least   squares,   K-class   estimators,  
• Limited Information and Full Information Maximum Likelihood Methods,  
• Three  stage  least  squares,  Generalized  least  squares,  Recursive  models,  SURE Models. Mixed Estimation  Methods, use of instrumental variables,  pooling   of   cross-section   and   time   series   data,   Principal   Component  Methods.  
• UNIT IV
• Problem and Construction of index numbers and their tests; fixed and chain  based index numbers; Construction of cost of living index number.  
• UNIT V
• Demand analysis - Demand and Supply Curves; Determination of demand  curves  from  market  data.  Engel's  Law  and  the  Engel's  Curves,  Income  distribution   and   method   of   its   estimation,   Pareto's   Curve,  Income inequality measures.  

 

Suggested Readings 

• Croxton FE & Cowden DJ. 1979. Applied General Statistics. Prentice Hall  of India.  
• Johnston J. 1984. Econometric Methods. McGraw Hill.  
• Judge   GC,   Hill   RC,   Griffiths   WE,   Lutkepohl   H   &   Lee   TC.   1988.  nd  
• Ed. Introduction  to  the  Theory  and  Practice  of  Econometrics.  2 John Wiley. 
• Kmenta J. 1986. Elements of Econometrics. 2    Ed. University of Michigan  nd  Press.  
• Koop G. 2007. Introduction to Econometrics. John Wiley. rd 
• Maddala GS. 2001. Introduction to Econometrics. 3   Ed. John Wiley.  
• Pindyck  RS  &  Rubinfeld  DL.  1998.  Econometric  Models  and  Economic Forecasts. 4   Ed. McGraw Hill. th rd 
• Verbeek M. 2008. A Guide to Modern Econometrics. 3   Ed. John Wiley.  

 

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STATISTICAL QUALITY CONTROL

Objective  

• This   course   is   meant   for   exposing   the   students   to   the   concepts   of  Statistical Quality Control and their applications in agribusiness and agro-  processing  industries.  This  course  would  enable  the  students  to  have  an  idea about the statistical techniques used in quality control. students who  do not have sufficient background of Statistical Methods.  

 

Theory  

• UNIT I
• Introduction  to Statistical Quality  Control; Control Charts for Variables - Mean,  Standard  deviation  and  Range  charts;  Statistical  basis;  Rational subgroups. 
• UNIT II
• Control charts for attributes- 'np', 'p' and 'c' charts. UNIT III
• Fundamental  concepts  of  acceptance,  sampling  plans,  single,  double  and sequential sampling plans for attributes inspection. 
• UNIT IV
• Sampling  inspection  tables  for  selection  of  single  and  double  sampling plans. 

 

Suggested Readings  

• Cowden DJ.  1957. Statistical Methods in Quality Control. Prentice Hall of India. 
• Dodge HF & Romig HG. 1959. Sampling Inspection Tables.  John Wiley. 
• Duncan A.J. 1986. Quality Control and Industrial Statistics. 5th Ed. Irwin Book Co. 
• Grant  EL  &  Leavenworth  RS.  1996.  Statistical  Quality  Control.  7    Ed. th  McGraw Hill. 
• Montgomery DC. 2005. Introduction to Statistical Quality Control. 5   Ed. th  John Wiley. 
• Wetherill  G.B.  1977.  Sampling  Inspection  and  Quality  Control.  Halsted Press. 

 

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OPTIMIZATION TECHNIQUES

Objective  

• This course is meant for exposing the students to the mathematical details  of  the  techniques  for  obtaining  optimum  solutions  under  constraints  for  desired  output.  They  will  be  taught  numerical  methods  of  optimization,  linear   programming   techniques,   non-linear   programming   and   multiple  objective   programming.   Students   will   also   be   exposed   to   practical  applications of these techniques.  

 

Theory 

• UNIT I
• Classical    Optimization    Techniques:    Necessary    Conditions    for    an  
• Extremum.   Constrained   Optimization:   Lagrange   Multipliers,   Statistical  Applications.    Optimization  and  Inequalities.    Classical  Inequalities,  like  Cauchy-Schwarz Inequality, Jensen Inequality and Markov Inequality.  
• UNIT II
• Numerical  Methods  of  Optimization:   Numerical  Evaluation  of  Roots  of  Equations, Direct Search Methods, Sequential Search Methods -- Fibonacci  
• Search Method.   Random Search Method - Method of Hooke and Jeeves,  
• Simplex  Search  Method.   Gradient  Methods,  like  Newton's  Method,  and  
• Method  of  Steepest  Ascent.    Nonlinear  Regression  and  Other  Statistical  Algorithms, like Expectation - Maximization Algorithm.  
• UNIT III
• Linear    programming    Techniques    -    Simplex    Method,    Karmarkar's  
• Algorithm, Duality and Sensitivity Analysis.   Zero-sum Two-person Finite  Games   and   Linear   Programming.  Integer   Programming.  Statistical Applications.  
• UNIT IV
• Nonlinear   Programming   and   its   Examples.       Kuhn-Tucker   Conditions.  
• Quadratic  Programming.    Convex  Programming.              Basics  of  Stochastic  
• Programming.             Applications.   Elements         of         Multiple    Objective  
• Programming.  Dynamic   Programming,   Optimal   Control   Theory   -  Pontryagin's Maximum Principle, Time-Optimal Control Problems.  

 

Practical 

• Problems  based  on  classical  optimization  techniques;  Problems  based  on  optimization  techniques  with  constraints;  Minimization  problems  using  numerical methods; Linear programming (LP) problems through graphical  method;  LP  problem  by  Simplex  method;  LP  problem  using  simplex  method  (Two-phase  method); LP  problem using  primal  and  dual  method;  Sensitivity   analysis   for   LP   problem;   LP   problem   using   Karmarkar's  method;  Problems  based  on  Quadratic  programming;  Problems  based  on  Integer    programming;    Problems    based    on    Dynamic    programming;  Problems based on Pontryagin's Maximum Principle.  

 

Suggested Readings  

• Rao  SS.  2007.  Engineering  Optimization:  Theory  and  Practice.  3  rd Ed. New Age.  
• Rustagi JS. 1994. Optimization Techniques in Statistics. Academic Press.
• Taha  HA.  2007.  Operations  Research:  Introduction  with  CD.  8 Pearson Edu. 
• Zeleny M. 1974. Linear Multiobjective Programming. Springer. 

 

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DEMOGRAPHY

Objective  

• This course is meant for training the students in measures of demographic  indices,   estimation   procedures   of   demographic   parameters.   Students  would also be exposed to population projection techniques and principles  involved in bioassays.  

 

Theory 

• UNIT I
• Introduction to vital statistics, crude and standard mortality and morbidity  rates,  Estimation  of  mortality,  Measures  of  fertility  and  mortality,  period  and cohort measures.  
• UNIT II
• Life tables and their applications, methods of construction of abridged life  tables, Increment-Decrement Life Tables.  
• UNIT III
• Stationary and stable populations, Migration and immigration. Application  of   stable   population   theory   to   estimate   vital   rates,   migration   and   its  estimation. Demographic relations in Nonstable populations. Measurement  of  population  growth,  Lotka's  model(deterministic)  and  intrinsic  rate  of  growth, Measures of mortality and morbidity, Period and  
• UNIT IV
• Principle of biological assays, parallel line and slope ratio assays, choice of  doses   and   efficiency   in   assays   quantal   responses,   probit   and   logit  transformations, epidemiological models.  

 

Suggested Readings 

• Cox DR. 1957.  Demography. Cambridge Univ. Press.  
• Finney DJ. 1981. Statistical Methods in Biological Assays. Charles Griffin.  
• Fleiss JL. 1981. Statistical Methods for Rates and Proportions. John Wiley.  
• Lawless JF. 1982. Statistical Models and Methods for Lifetime Data. John  Wiley.  
• MacMahon  B  &  Pugh  TF.  1970.  Epidemiology-  Principles  and  Methods.  Little Brown, Boston.  
• Mann NR, Schafer RE & Singpurwalla ND. 1974. Methods for Statistical Analysis of Reliability and Life Data. John Wiley.  
• Newell C. 1988. Methods and Models in Demography. Guilford Publ.  
• Preston S, Heuveline P & Guillot M. 2001. Demography: Measuring and Modeling Population Processes. Blackwell Publ.  
• Rowland DT. 2004. Demographic Methods and Concepts. Oxford Press.  
• Siegel   JS   &   Swanson   DA.   2004.   The   Methods   and   Material   of Demography. 2    Ed. Elsevier.  
• Woolson  FR.  1987.  Statistical  Methods  for  the  Analysis  of  Biomedical Data. John Wiley.  

 

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STATISTICAL METHODS FOR LIFE SCIENCES  

Objective  

• This  course  focuses  on  statistical  methods  for  discrete  data  collected  in  public  health,  clinical  and  biological  studies  including  survival  analysis.  This  would  enable  the  students  to  understand  the  principles  of  different  statistical techniques useful in public health and clinical studies conducted.  

 

Theory 

• UNIT I
• Proportions and counts, contingency tables, logistic regression models,  Poisson regression and log-linear models, models for polytomous data and  generalized linear models.  
• UNIT II
• Computing    techniques,    numerical    methods,    simulation    and    general  implementation of biostatistical analysis techniques with emphasis on data  applications.  Analysis  of  survival  time  data  using  parametric  and  non-  parametric models, hypothesis testing, and methods for analyzing censored  (partially    observed)   data   with   covariates.   Topics   include   marginal  estimation of  a  survival  function,  estimation  of  a  generalized  multivariate  linear regression model (allowing missing covariates and/or outcomes).  
• UNIT III
• Proportional Hazard model: Methods of estimation, estimation of survival  functions,   time-dependent   covariates,   estimation   of   a   multiplicative  intensity model (such as Cox proportional hazards model) and estimation of  causal parameters assuming marginal structural models.  
• UNIT IV
• General theory for developing locally efficient estimators of the parameters  of   interest   in   censored   data   models.   Rank   tests   with   censored   data.  Computing    techniques,    numerical    methods,    simulation    and    general  implementation of biostatistical analysis techniques with emphasis on data  applications.  
• UNIT V
• Newton,   scoring,   and   EM   algorithms   for   maximization;   smoothing  methods;  bootstrapping;  trees  and  neural  networks;  clustering;  isotonic  regression; Markov chain Monte Carlo methods.  

 

Suggested Readings 

• Biswas   S.   1995.   Applied   Stochastic   Processes.   A   Biostatistical   and Population Oriented Approach. Wiley Eastern Ltd.  
• Collett D. 2003. Modeling Survival Data in Medical Research. Chapman &  Hall.  
• Cox DR  & Oakes D. 1984. Analysis of Survival Data. Chapman &  Hall.  
• Hosmer   DW   Jr.   &   Lemeshow   S.   1999.   Applied   Survival   Analysis: Regression Modeling or Time to Event. John Wiley.  
• Klein  JP  &  Moeschberger  ML.  2003.  Survival  Analysis:  Techniques  for Censored and Truncated Data. Springer.  
• Kleinbaum DG & Klein M 2005. Survival Analysis. A Self Learning Text.  Springer.  
• Kleinbaum DG & Klein M. 2005. Logistic Regression. 2nd Ed. Springer.  
• Lee ET. 1992. Statistical Methods for Survival Data Analysis. John Wiley.  Miller RG. 1981. Survival Analysis. John Wiley.  
• Therneau TM & Grambsch PM. 2000. Modeling Survival Data: Extending the Cox Model.  Springer.  

 

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STATISTICAL ECOLOGY

Objective  

• This course is meant for exposing the students to the importance and use of  statistical  methods  in  collections  of  ecological  data,  species-abundance  relations, community classification and community interpretation.  

 

Theory 

• UNIT I
• Ecological      data,      Ecological   sampling;      Spatial      pattern   analysis:  Distribution methods, Quadrant-variance methods,  Distance methods.  
• UNIT II
• Species-abundance   relations:   Distribution    models,   Diversity    indices;  Species     affinity:     Niche-overlap     indices,     interspecific     association,  interspecific covariation.  
• UNIT III
• Community  classification:    Resemblance  functions,  Association  analysis,  Cluster   analysis;   Community   Ordination:   Polar   Ordination,   Principal  Component Analysis, Correspondence analysis, Nonlinear ordination.  
• UNIT IV
• Community   interpretation:   Classification   Interpretation   and   Ordination  Interpretation.  

 

Suggested Readings 

• Pielou EC.  1970. An introduction to Mathematical Ecology. John Wiley.  
• Reynolds   JF   &   Ludwig   JA.   1988.   Statistical   Ecology:   A   Primer   on Methods and Computing. John Wiley.  
• Young LJ, Young JH & Young J. 1998. Statistical Ecology: A Population Perspective. Kluwer.  

 

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ADVANCED STATISTICAL COMPUTING

Objective  

• This is an advanced course in Statistical Computing that aims at describing  some  advanced  level  topics  in  this  area  of  research  with  a  very  strong  potential of applications. This course also prepares students for undertaking  research  in  this  area.  This  also  helps  prepare  students  for  applications  of  this   important   subject   to   agricultural   sciences   and   use   of   statistical  packages.  

 

Theory 

• UNIT I
• Measures of association. Structural models for discrete data in two or more  dimensions.  
• Estimation   in   complete   tables.   Goodness   of   fit,   choice   of   a   model.  Generalized   Linear   Model   for   discrete   data,   Poisson   and   Logistic  regression models. Log-linear models.  
• UNIT II
• Elements  of  inference  for  cross-classification  tables.  Models  for  nominal  and ordinal response.  
• UNIT III
• Computational   problems   and   techniques   for   robust   linear   regression,  nonlinear   and   generalized   linear   regression   problem,   tree-structured  regression   and  classification,  cluster   analysis,  smoothing   and  function  estimation, robust multivariate analysis.  
• UNIT IV
• Analysis    of    incomplete    data:    EM    algorithm,    single    and    multiple  imputations. Markov Chain, Monte Carlo and annealing techniques, Neural  Networks, Association Rules and learning algorithms.  
• UNIT V
• Linear mixed effects models, generalized linear models for correlated data  (including  generalized  estimating  equations),  computational  issues  and  methods for fitting models, and dropout or other missing data.  
• UNIT VI
• Multivariate  tests  of  linear  hypotheses,  multiple  comparisons,  confidence  regions,    prediction    intervals,    statistical    power,    transformations    and  diagnostics, growth curve models, dose-response models.  

 

Practical 

• Analysis   of   qualitative   data;   Generalized   linear   for   correlated   data;  Generalized linear models for discrete data; Robust methods of estimation  and  testing   of  non-normal  data;   Robust   multivariate   analysis;  Cluster  analysis;  Analysis  of  Incomplete  data;  Classification  and  prediction  using  artificial neural networks; Markov Chain; Analysis of data having random  effects  using  Linear  mixed  effects  models;  Analysis  of  data  with  missing  observations;  Applications  of  multiple  comparison  procedures;  Building  Simultaneous  confidence  intervals;  Fitting  of  growth  curve  models  to  growth data; Fitting of dose-response curves and estimation of parameters.  

 

Suggested Readings  

• Everitt BS & Dunn G. 1991. Advanced Multivariate Data Analysis. 2    Ed.  nd  Arnold.  
• Geisser S. 1993. Predictive Inference: An Introduction. Chapman & Hall.  
• Gentle  JE,  Härdle  W  &  Mori  Y.  2004.  Handbook  of  Computational Statistics -Concepts and Methods. Springer.  
• Han J & Kamber M. 2000. Data Mining: Concepts and Techniques.  Morgan.  
• Hastie  T,  Tibshirani  R  &  Friedman  R.  2001.  The  Elements  of  Statistical Learning: Data Mining, Inference and Prediction. Springer.  
• Kennedy WJ & Gentle JE. 1980. Statistical Computing. Marcel Dekker.  
• Miller  RG  Jr.  1986.  Beyond  ANOVA,  Basics  of  Applied  Statistics.  John  Wiley.  
• Rajaraman V. 1993. Computer Oriented Numerical Methods. Prentice-Hall.  
• Robert  CP  &  Casella  G.  2004.  Monte  Carlo  Statistical  Methods.  2 Springer. 
• Ross S. 2000. Introduction to Probability Models. Academic Press. 
• Simonoff JS. 1996. Smoothing Methods in Statistics. Springer. 
• Thisted RA. 1988. Elements of Statistical Computing. Chapman & Hall. 
• Venables WN & Ripley BD. 1999. Modern Applied Statistics With S-Plus. 3   Ed. Springer.  
• Free Statistical Softwares: http://freestatistics.altervista.org/en/stat.php.  
• Design Resources Server: www.iasri.res.in.  
• SAS Online Doc 9.1.3:  http://support.sas.com/onlinedoc/913/docMainpage.jsp  

 

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SIMULATION TECHNIQUES

Objective  

• This course is meant for students who have a good knowledge in Statistical  Inference and   Statistical Computing.   This course would   prepare students  for  undertaking  research  in  the  area  of  simulation  techniques  and  their  applications to agricultural sciences.  

 

Theory 

• UNIT I
• Review of simulation methods; Implementation of simulation methods - for  various    probability    models,    and    resampling    methods:    theory    and  application of the jackknife and the bootstrap.  
• UNIT II
• Randomization    tests,    analysis    using    computer    software    packages.  Simulating multivariate distributions, MCMC methods and Gibbs sampler.  
• UNIT III
• Correlograms, periodograms, fast Fourier transforms, power spectra, cross-  spectra, coherences, ARMA and transfer-function models, spectral-domain  regression.  Simulated  data  sets  to  be  analyzed  using  popular  computer  software packages  
• UNIT IV
• Stochastic   simulation:   Markov   Chain,   Monte   Carlo,   Gibbs'   sampling,  Hastings-Metropolis   algorithms,   critical   slowing-down   and   remedies,  auxiliary  variables,  simulated  tempering,  reversible-  jump  MCMC  and  multi-grid methods.  

 

Practical  

• Simulation    from    various    probability    models;    Resampling    methods, jackknife  and  the  bootstrap;  Randomization  tests;  Simulating  multivariate distributions,    MCMC    methods    and    Gibbs    sampler;    Correlograms, periodograms,   fast   Fourier   transforms,   power   spectra,   cross-spectra, coherences;    ARMA    and    transfer-function    models,    spectral-domain regression;  Simulated  data  sets  to  be  analyzed  using  popular  computer software   packages;   Markov   Chain,   Monte   Carlo,   Gibbs'   sampling; Reversible- jump MCMC and multi-grid methods. 

 

Suggested Readings  

• Averill  ML,  Kelton   D.  2005.  Simulation,  Modeling  and  Analysis.  Tata McGraw Hill. 
• Balakrishnan  N,  Melas  VB  &  Ermakov  S.  (Ed.).  2000.  Advances  in Stochastic Simulation Methods. Basel-Birkhauser. 
• Banks  J.  (Ed.).  1998.  Handbook  of  Simulation:  Principles,  Methodology, Advances, Applications and Practice. John Wiley. 
• Brately P, Fox BL & Scharge LE. 1987. A Guide to Simulation.  Springer. 
• Davison   AC   &   Hinkley   DV.   2003.   Bootstrap   Methods   and   their Application. Cambridge Univ. Press. 
• Gamerman D, Lopes HF & Lopes HF.  2006. Markov Chain Monte Carlo: 
• Stochastic Simulation for Bayesian Inference. CRC Press. 
• Gardner FM & Baker JD. 1997.  Simulation Techniques Set. John Wiley. 
• Gentle JE. 2005. Random Number Generation and Monte Carlo Methods. Springer. 
• Janacek   G   &   Louise   S.   1993.   Time   Series:   Forecasting,   Simulation, Applications.   Ellis   Horwood   Series   in   Mathematics   and   Its Applications. 
• Kleijnen J & Groenendaal WV. 1992. Simulation: A Statistical Perspective. John Wiley. 
• Kleijnen   J.   1974   (Part   I),   1975   (Part   II).   Statistical   Techniques   in Simulation. Marcel Dekker. 
• Law  A  &  Kelton  D.  2000.   Simulation  Modeling  and  Analysis.  McGraw Hill. 
• Press WH, Flannery BP, Tenkolsky SA & Vetterling WT. 1986. Numerical Recipes.  Cambridge Univ. Press. 
• Ripley BD. 1987. Stochastic Simulation. John Wiley. Ross SM. 1997. Simulation. John Wiley. 

 

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ADVANCED STATISTICAL METHODS

Objective  

• This  is  an  advanced  course  in  Statistical  Methods  that  aims  at  describing  some  advanced  level  topics  in  this  area  of  research  with  a  very  strong  potential of applications. This course also prepares students for undertaking  research  in  this  area.  This  also  helps  prepare  students  for  applications  of  this important subject to agricultural sciences.  

 

Theory 

• UNIT I
• Ridge   regression:   Basic   form,   Use   as   a   selection   procedure.   Robust  regression:   Least   absolute   deviations   regression,   M-estimators,   Least  median of squares regression. Nonparametric regression.  
• UNIT II
• Introduction  to  the  theory  and  applications  of  generalized  linear  models,  fixed  effects,  random  effects  and  mixed  effects  models,  estimation  of  variance  components  from  unbalanced  data.  Unified  theory  of  least  -  squares, MINQUE, MIVQUE, REML.  UNIT III
• Quasi-likelihoods,    and    generalized    estimating    equations    -    logistic  regression,    over-dispersion,    Poisson    regression,    log-linear    models,  conditional    likelihoods,    generalized    mixed    models,    and    regression  diagnostics. Theory of statistical methods for analyzing categorical data by  means   of   linear   models;   multifactor   and   multi-response   situations;  interpretation of interactions.  
• UNIT IV
• Fitting   of   a   generalized   linear   model,   mixed   model   and   variance  components estimation, MINQUE, MIVQUE, REML.  
• UNIT V
• Fitting  of Logistic regression, Poisson regression, ridge regression, robust  regression, non-parametric regression.  

 

Suggested Readings 

• Chatterjee  S,  Hadi  A  &  Price  B.1999.  Regression  Analysis  by  Examples.  John Wiley.  
• Draper  NR  &  Smith  H.  1998.  Applied  Regression  Analysis.  3    Ed.  John  rd Wiley. 
• Rao  CR.  1965.   Linear  Statistical  Inference  and  its  Applications.  2  nd  Ed. John Wiley.  
• Searle SR, Casella G & McCulloch CE. 1992. Variance Components. John  Wiley.  
• Searle SR. 1971.  Linear Models. John Wiley.  

 

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ADVANCED STATISTICAL INFERENCE

Objective  

• This  course  aims  at  describing  the  advanced  level  topics  in  statistical  methods  and  statistical  inference.  This  course  would  prepare  students  to  have  a  strong  base  in  basic  statistics  that  would  help  them  in  undertake  basic and applied research in Statistics.  

 

Theory 

• UNIT I
• Robust estimation and  robust tests,  Robustness, M-estimates. L-estimates,  asymptotic   techniques,   Bayesian   inference.   Detection   and  handling   of  outliers in statistical data.  
• UNIT II
• Loglinear models, saturated models, hierarchical models, Analysis of multi  -  dimensional  contingency  tables.  Non-parametric  maximum  likelihood  estimation.  
• UNIT III
• Density    Estimation:       Density    Estimation    in    the    Exploration    and  
• Presentation  of Data. Survey  of existing  methods. The Kernel  method for  
• Univariate   Data:   Rosenblatts   naïve   estimator,   its   bias   and   variance.  
• Consistency  of  general  Kernel  estimators,  MSE  and  IMSE.  Asymptotic  
• normality  of  Kernel  estimates  of  density.  Estimation  of  distribution  by  method of kernels.  
• UNIT IV
• Consistency    and   asymptotic   normality    (CAN)   of   real    and    vector  parameters.  Invariance  of  consistency  under  continuous  transformation.  Invariance   of   CAN   estimators   under   differentiable   transformations,  generation  of  CAN  estimators  using  central  limit  theorem.  Exponential  class   of   densities   and   multinomial   distribution,   Cramer-Huzurbazar  theorem, method of scoring.  
• UNIT V
• Efficiency: asymptotic relative efficiency and Pitman's theorem. Concepts  and examples of Bahadur efficiency and Hodges-Lehmanns efficiency with  examples.  The  concepts  of  Rao's  second  order  efficiency  and  Hodges-  Lehmann's  Deficiency    with    examples.  Rank  tests,  permutation  tests,  asymptotic  theory  of  rank  tests  under  null  and  alternative  (contiguous)  hypotheses.  
• UNIT VI
• Inference on Markov Chains:   Maximum likelihood estimation and testing  of Transition Probability Matrix of a Markov Chain, testing for order of a  Markov chain, estimation of functions of transition probabilities.  
• UNIT VII
• Concept  of  loss,  risk   and  decision  functions,   admissible  and  optimal  decision functions, a-priori and posteriori distributions, conjugate families.  Bayes   and   Minimax   decision   rules   and   some  basic   results   on   them.  
• Estimation  and  testing  viewed  as  cases  of  decision  problems.   Bayes  and  Minimax decision functions with applications to estimation with quadratic  loss  function.  Concept  of  Bayesian  sequential  analysis.  Bayes  sequential  decision  rule.  The  SPRT  as  a  Bayes  procedure.  Minimax  sequential  procedure. 
• UNIT VIII
• U-Statistics:    definitions    of    estimable    parametric    function,    kernel,  symmetric kernel and U-statistics. Variance and covariance of U-statistics.  Hoeffding's decomposition of U-statistics -examples.  U-statistics based on  sampling from finite populations and weighted U-statistics with examples.  Some  convergence  results  on  U-statistics.    Asymptotic  normality  of  U-  statistics with examples.  
• UNIT IX
• Resampling  Plans  :   Estimation  of  standard  and biased  deviation  of point  estimator  by  the  Jackknife,  the  Bootstrap,  the  Infinitesimal  Jackknife,  the  Delta  and  the  Influence  function  methods.  Estimation  of  excess  error  in  regression   by   cross   validation,   the   Jackknife   and   Bootstrap   methods.  Nonparametric   confidence   interval   for   the   median   by   the   Percentile  method.  

 

Suggested Readings 

• Casela  G  &  Berger  RL.  2001.  Statistical  Inference.  Duxbury  Thompson  Learning.  
• Daniel  W.1990.  Applied  Nonparametric  Statistics.            Houghton  Mifflin,  Boston.  
• DeGroot MH. 1970. Optimal Statistical Decisions. McGraw Hill.  
• Efron  B  &  Tibshirani  RJ.  1993.  An  Introduction  to  Bootstrap.  Chapman  Hall/CRC.  
• Ferguson TS. 1967. Mathematical Statistics, A Decision Theoretic Approach. Academic Press.  
• Gibbons JD & Chakraborty S. 1992. Non-parametric Statistical Inference.  Marcel Dekker.  
• Gray  HL  &  Schucany  WR.1972.  The  Generalized  Jackknife  Statistics.  Marcel Dekker.  
• Kale BK.1999. A First Course on Parametric Inference. Narosa Publ.  
• Prakasa Rao BLS. 1983. Nonparametric Functional Estimation. Academic  Press.  
• Rao CR.1965. Linear Statistical Inference and its Applications. 2    Ed.  nd  John Wiley.  
• Silverman BW. 1986. Density Estimation for Statistics and Data Analysis.  
• Chapman & Hall.  
• Silvey SD. 1975. Statistical Inference. Chapman & Hall.  
• Tapia  RA  &  Thompson  JR.  1978.  Nonparametric  Probability  Density Estimation. Johns Hopkins Univ. Press.  
• Tiku  ML,  TanWY  &  Balakrishnan  N.  1986.  Robust  Inference.  Marcel  Dekker.  
• Wald A. 2004. Sequential Analysis.  Dover Publ.  
• Wasserman L. 2006. All of Nonparametric Statistics. Springer.  

 

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ADVANCED DESIGN OF EXPERIMENTS

Objective  

• This   is   an   advanced   course   in   Design   of   Experiments   that   aims   at  describing  some  advanced  level  topics  for  students  who  wish  to  pursue  research  in  Design  of  Experiments.  This  course  prepares  students  for  undertaking  research  in  this  area.  This  also  helps  prepare  students  for  applications of this important subject to agricultural sciences.  

 

Theory 

• UNIT I
• General  properties  and  analysis  of  block  designs.  Balancing  criteria.  m-  associate  PBIB  designs,  and  their  association  schemes  including  lattice  designs - properties and construction, Designs for test treatment - control(s)  comparisons; Nested block designs, Mating designs.  UNIT II
• General properties and analysis of two-way heterogeneity designs, Youden  type   designs,   generalized   Youden   designs,   Pseudo   Youden   designs.  Structurally Incomplete block designs, Designs for two sets of treatments.  
• UNIT III
• Balanced factorial experiments - characterization and analysis (symmetrical  and asymmetrical factorials). Factorial experiments with extra treatment(s).  Orthogonal  arrays,  Mixed  orthogonal  arrays,  balanced  arrays,  Fractional  replication, Regular and irregular fractions.  
• UNIT IV
• Response   surface   designs   -   Symmetrical   and   asymmetrical   factorials,  Response optimization and slope estimation, Blocking. Canonical analysis  and   ridge   analysis.   Experiments   with   mixtures:   design   and   analysis.  Experiments with qualitative cum quantitative factors.  
• UNIT V
• Optimality criteria and optimality of designs, robustness of designs against  loss of data, outliers, etc. Diagnostics in design of experiments.  

 

Suggested Readings 

• Chakraborti    MC.    1962.    Mathematics    of    Design    and    Analysis    of Experiments. Asia Publ. House.  
• Dean AM & Voss D. 1999. Design and Analysis of Experiments. Springer.  
• Dey A & Mukerjee R. 1999. Fractional Factorial Plans. John Wiley.  
• Dey A 1986. Theory of Block Designs. Wiley Eastern.  
• Hall M Jr. 1986. Combinatorial Theory. John Wiley.  
• Hedayat AS,  Sloane NJA  &  Stufken J.  1999.  Orthogonal  Arrays: Theory and Applications. Springer.  
• John  JA  &  Quenouille  MH.  1977.  Experiments:  Design  and  Analysis.  Charles & Griffin.  
• Khuri AI & Cornell JA. 1996. Response Surface Designs and Analysis. 2  nd  Ed. Marcel Dekker.  
• Montgomery DC. 2005. Design and Analysis of Experiments. John Wiley.  
• Ogawa J. 1974. Statistical Theory of the Analysis of Experimental Designs.  Marcel Dekker.  
• Parsad R, Gupta VK, Batra PK, Satpati SK & Biswas P. 2007. Monograph on α-designs. IASRI, New Delhi.  
• Raghavarao D. 1971. Construction and Combinatorial Problems in Design of Experiments. John Wiley.  
• Shah KR & Sinha BK.  1989. Theory of Optimal Designs.  Lecture notes in Statistics. Vol. 54. Springer.  
• Street  AP  &  Street  DJ.  1987.  Combinatorics  of  Experimental  Designs.  Oxford Science Publ.  
• Design Resources Server: www.iasri.res.in.  

 

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ADVANCED SAMPLING TECHNIQUES  

Objective  

• This is an advanced course in Sampling Techniques that aims at describing  some  advanced  level  topics  for  students  who  wish  to  pursue  research  in  Sampling   Techniques.   This   course   prepares   students   for   undertaking  research  in  this  area.  This  also  helps  prepare  students  for  applications  of  this important subject to Statistical System in the country.  

 

Theory 

• UNIT I
• Controlled  selection.  Two  way  stratification,  collapsed  strata.  Systematic  sampling in two dimensions. Use of combinatorics in controlled selection.  Integration of surveys - Lahiri and Keyfitz's procedures.  
• UNIT II
• Variance   estimation   in   complex   surveys.   Taylor's   series   linearisation,  balanced repeated replication, Jackknife and bootstrap methods.  
• UNIT III
• Unified theory of sampling from finite populations. UMV - Non-existence  theorem  and  existence  theorem  under  restricted  conditions.  Concept  of  sufficiency  and  likelihood  in  survey  sampling.  Admissibility  and  hyper-  admissibility.  
• UNIT IV
• Inference  under  super  population  models  -  concept  of  designs  and  model  unbiasedness, prediction approach. Regression analysis and categorical data  analysis  with  data  from  complex  surveys.  Domain  estimation.  Small  area  estimation.  
• UNIT V
• Stochastic  parameter  models,  Bayes'  linear  predictor,  Bayesian  models  with  multi-stage  sampling.  Measurement  error  and  small  area  estimation,  Time  series  approach  in  survey  sampling.  Dynamic  Bayesian  prediction,  Kalman  filter,  Empirical  and  Hierarchical  Bayes predictors,  Robust linear  prediction, Bayesian robustness.  

 

Suggested Readings 

• Berger   JO.   1993.   Statistical   Decision   Theory   and   Bayesian   Analysis.  Springer.  
• Bolfarine  H  &  Zacks  S.  1992.  Prediction  Theory  for  Finite  Population Sampling. Springer.  
• Cassel CM, Sarndal CE & Wretman JH. 1977. Foundations of Inference in Survey Sampling. John Wiley.  
• Des Raj & Chandhok P. 1998. Sample Survey Theory. Narosa Publ. House.  
• Ghosh  M  &  Meeden  G.  1997.  Bayesian  Method  for  Finite  Population Sampling.     Monograph   on   Statistics   and   Applied   Probability.  Chapman & Hall.  
• Mukhopadhyay P. 1998. Theory and Methods of Survey Sampling. Prentice  Hall of India.  
• Rao JNK. 2003. Small Area Estimation. John Wiley.  
• Sarndal  CE,  Swensson  B  &  Wretman  JH.  1992.  Model  Assisted  Survey Sampling. Springer.  

 

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ADVANCED STATISTICAL GENETICS 

Objective  

• This  is  an  advanced  course  in  Statistical  Genetics  that  aims  at  describing  some  advanced  level  topics  for  students  who  wish  to  pursue  research  in  Statistical Genetics. This course prepares students for undertaking research  in  this  area.  This  also  helps  prepare  students  for  applications  of  this  important subject in plant and animal breeding.  

 

Theory 

• UNIT I
• Hardy-Weinberg  law  with  multiple  allelic  systems,  auto-tetraploids  and  self-sterility alleles. Complex cases of selection with two or more loci.  
• UNIT II
• Different  approaches  to  study  inbreeding  process,  methods  of  path  co-  efficient,    probability    and    generation    matrix.    Fisher's    approach    to  inbreeding. Stochastic process of gene frequency change, transition matrix  approach  using  finite  Markov  chains,  diffusion  approximation,  Steady  decay and distribution of gene frequency, Probability of fixation of a gene,  Conditional process - Markov chains and diffusion approaches, Distribution  of time until fixation, random fluctuations in selection intensity, stationary  distribution of gene frequency. Effective population size.  
• UNIT III
• Prediction and estimation of genetic merit. Best linear unbiased prediction,  Use of mixed model methodology in analysis of animal and plant breeding  experiments.  Newer  reproductive  technology  and  its  effect  in  genetic  evaluation of individual merit. Estimation of genetic parameters - problems  relating   to   computational   aspects   of   genetic   variance   components,  parameter  estimation  in  variance  component  models  for  binary  response  data.  
• UNIT IV
• Identification of genes with large effects, Use of molecular markers (RFLP,  PCR-AFLP,  RAPD  and  SSR),  Gene  mapping  and  Quantitative  trait  loci.  
• Molecular manipulation for genetic variability.  
• UNIT V
• Survival analysis and concept of censored observation in animal breeding.  Phylogeny and analysis of molecular variance.  

 

Suggested Readings 

• Crow  JF  &  Kimura  M.  1970.  An  Introduction  of  Population  Genetics Theory. Harper & Row.  
• Ewens WJ. 1979. Mathematical Population Genetics. Springer.  
• Falconer DS. 1985. Introduction to Quantitative Genetics. ELBL.  
• Fisher RA. 1949. The Theory of Inbreeding.  Oliver & Boyd.  
• Fisher RA. 1958. The Genetical Theory of Natural Selection. Dover Publ.  
• Haldane JBS. 1932. The Causes of Evolution. Harper & Bros.  
• Kempthorne O. 1957. An Introduction to Genetic Statistics. The Iowa State  Univ. Press.  
• Lerner    IM.    1950.    Population    Genetics    and    Animal    Improvement.  Cambridge Univ. Press.  
• Lerner IM. 1958. The Genetic Theory of Selection. John Wiley.  
• Li CC. 1982. Population Genetics. The University of Chicago Press.  
• Mather K & Jinks JL. 1982. Biometrical Genetics. Chapman & Hall.  
• Mather K. 1951.  The Measurement of Linkage in Heredity. Methuen.  
• Nagilaki   T.   1992.   Introduction   to   Theoretical   Population   Genetics.  Springer.  
• Narain P. 1990. Statistical Genetics. Wiley Eastern.  

 

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STATISTICAL MODELING

Objective  

• This  is  an  advanced  course  in  Statistical  Methods  that  aims  at  describing  some  advanced  level  topics  in  this  area  of  research  with  a  very  strong  potential of applications. This course also prepares students for undertaking  research  in  the  area  of  empirical  and  mechanistic  models  and  nonlinear  estimation   and   the   replications   in   different   disciplines   of   agricultural  sciences.  

 

Theory 

• UNIT I
• Empirical   and    mechanistic    models.   Nonlinear   growth    models    like  monomolecular,  logistic,  Gompertz,  Richards.  Applications  in  agriculture  and fisheries.  
• UNIT II
• Nonlinear  estimation:  Least  squares  for  nonlinear  models,  Methods  for  estimation   of   parameters   like   Linearization,   Steepest,   and   Levenberg-  Marquardt's Reparameterization.  
• UNIT III
• Two-species  systems.  Lotka-Volterra,  Leslie-Gower  and  Holling-Tanner  non-linear  prey-predator  models.  Volterra's  principle  and  its  applications.  Gause competition model.  
• UNIT IV
• Compartmental  modelling  -  First  and  second  order  input-output  systems,  Dynamics of a multivariable system.  

 

Practical 

• Fitting of mechanistic non-linear models; Application of Schaefer and Fox  non-linear models; Fitting of compartmental models.  

 

Suggested Readings 

• Draper  NR  &  Smith  H.  1998.  Applied  Regression  Analysis.  3    Ed.  John  rd Wiley.  
• Efromovich S. 1999. Nonparametric Curve Estimation. Springer.  
• Fan   J   &   Yao   Q.   2003.   Nonlinear   Time   Series-Nonparametric   and Parametric Methods. Springer.  
• France  J  &  Thornley  JHM.  1984.  Mathematical  Models  in  Agriculture.  Butterworths.  
• Harvey  AC.  1996.  Forecasting,  Structural  Time  Series  Models  and  the Kalman Filter. Cambridge Univ. Press.  
• Ratkowsky   DA.   1983.   Nonlinear   Regression   Modelling:   A   Unified Practical Approach. Marcel Dekker.  
• Ratkowsky DA. 1990. Handbook of Nonlinear Regression Models. Marcel  Dekker.  
• Seber GAF & Wild CJ. 1989. Non-linear Regression. John Wiley.  
• Silverman BW. 1986.  Density Estimation for Statistics and Data Analysis.  Chapman & Hall.  

 

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ADVANCED TIME SERIES ANALYSIS

Objective  

• This is an advanced course in Time Series Analysis that aims at describing  some  advanced  level  topics  in  this  area  of  research  with  a  very  strong  potential of applications. This course also prepares students for undertaking  research  in  this  area.  This  also  helps  prepare  students  for  applications  of  this important subject to agricultural sciences.  

 

Theory 

• UNIT I
• Multivariate  time  series:  modelling  the  mean,  stationary  VAR  models:  properties, estimation, analysis and forecasting, VAR models with elements  of    nonlinearity,    Non-stationary    multivariate    time    series:    spurious  regression, co-integration, common trends.  
• UNIT II
• Volatility: Modelling the variance, The class of ARCH models: properties,  estimation, analysis and forecasting, stochastic volatility, realized volatility,  Extensions:   IGARCH,   ARCH-t,   ARCD,   Multivariate   GARCH,   Time-  varying risk and ARCH-in-mean.  
• UNIT III
• Structural time-series modelling: State space models, Kalman filter. Local  level  model, Local linear trend  model, Seasonal  models, Cyclical models.  
• Nonlinear  time-series  models:  Parametric  and  nonparametric  approaches.  
• Autoregressive   conditional   heteroscedastic   model   and   its   extensions.  Threshold and Functional coefficient autoregressive models.  
• UNIT IV
• Nonlinear  programming,  Kuhn-Tucker  sufficient  conditions,  Elements  of  multiple objective programming,  Dynamic  Programming,  Optimal  control  theory - Pontryagin's maximum principle, Time-optimal control problems.  

 

Suggested Readings 

• Box   GEP,   Jenkins   GM   &   Reinsel   GC.   2008.   Time   Series   Analysis: 
• Forecasting and Control. 3   Ed. John Wiley. rd       
• Brockwell  PJ  &  Davis  RA.  1991.  Time  Series:  Theory  and  Methods.  2         nd Ed. Springer.  
• Chatfield  C.  2004.  The  Analysis  of  Time  Series:  An  Introduction.  6    Ed.  th  Chapman & Hall/CRC.  
• Tong  H.  1995.  Nonlinear  Time  Series:  A  Dynamical  System  Approach.  Oxford Univ. Press.  

 

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STOCHASTIC PROCESSES

Objective  

• This  is  a  course  on  Stochastic  Processes  that  aims  at  describing  some  advanced level topics in this area of research with a very strong potential of  applications. This course also prepares students for undertaking research in  this area. This also helps prepare students for applications of this important  subject to agricultural sciences.  

 

Theory 

• UNIT I
• Introduction  to  stochastic  process  -  classification  according  to  state  space  and   time   domain.   Finite   and   countable   state   Markov   chains;   time-  homogeneity;  Chapman-Kolmogorov  equations,  marginal  distribution  and  finite dimensional distributions. Classification of Markov chain.  Canonical  form  of  transition  probability  matrix  of  a  Markov  chain.    Fundamental  matrix;  probabilities  of  absorption  from  transient  states  into  recurrent  classes in a finite Markov chain, mean time for absorption.   Ergodic state  and Ergodic chain. Stationary distribution of a Markov chain, existence and  evaluation  of  stationary  distribution.    Random  walk  and  gamblers  ruin  problem.  
• UNIT II
• Discrete  state  continuous  time  Markov  process:  Kolmogorov  difference  -  differential  equations.   Birth  and  death  process,  pure  birth  process  (Yule-  Fury  process).   Immigration-Emigration  process.   Linear  growth  process,  pure death process.  
• UNIT III
• Renewal  process:  renewal  process  when  time  is  discrete  and  continuous.  Renewal function and renewal density.   Statements of Elementary renewal  theorem and Key renewal theorem.  
• UNIT IV
• Stochastic  process  in  biological  sciences:  Markov  models  in  population  genetics,  compartmental  analysis.     Simple  deterministic  and  stochastic  epidemic  model.    General  epidemic  models-Karmack  and  McKendrick's  threshold theorem. Recurrent epidemics.  
• UNIT V
• Elements  of  queueing  process;  the  queuing  model  M/M/1:  steady  state  behaviors.    Birth  and  death  process  in  queuing  theory-  Multi  channel  models.  Net work of Markovian queuing system. 
• UNIT VI
• Branching process: Galton-Watson branching process.   Mean and variance  of size of nth generation, probability of ultimate extinction of a branching  process. Fundamental theorem of branching process and applications.  
• UNIT VII
• Wiener process- Wiener process as a limit of random walk.   First passage  time  for  Wiener  process.    Kolmogorov  backward  and  forward  diffusion  equations and their applications.  

 

Suggested Readings 

• Adke SR & Manjunath SM. 1984. Finite Markov Processes. John Wiley.  
• Bailey NTJ. 1964.   Elements of Stochastic Processes with Applications to the Natural Sciences.  Wiley Eastern.  
• Bartlett MS. 1955. Introduction to Stochastic Processes. Cambridge Univ.  Press.  
• Basawa IV & Prakasa Rao BLS. 1980. Statistical Inference for Stochastic Processes. Academic Press.  
• Bharucha-Reid AT. 1960. Elements of the Theory of Markov Processes and their Applications. McGraw Hill.  
• Bhat BR. 2000. Stochastic Models; Analysis and Applications. New Age.  
• Cox   DR  &   Miller   HD.   1965.       The   Theory  of   Stochastic  Processes. Methuen.  
• Draper NR & Smith H. 1981. Applied Regression Analysis. Wiley Eastern.  
• France  J  &  Thornley  JHM.  1984.  Mathematical  Models  in  Agriculture.  
• Butterworths.  
• Karlin  S  &  Taylor  H.M.  1975.  A  First  Course   in  Stochastic  Processes.  Vol. I. Academic Press.  
• Lawler GF. 1995. Introduction to Stochastic Processes. Chapman & Hall.  
• Medhi J.  2001. Stochastic Processes. 2    Ed. Wiley Eastern.  
• Parzen E. 1962. Stochastic Processes. Holden-Day.  
• Prabhu NU. 1965. Stochastic Processes. Macmillan.  
• Prakasa  Rao  BLS  &  Bhat  BR.1996.  Stochastic  Processes  and  Statistical Inference. New Age.  
• Ratkowsky   DA.   1983.   Nonlinear   Regression   Modelling:   a   Unified Practical Approach. Marcel Dekker.  
• Ratkowsky DA. 1990. Handbook of Nonlinear Regression Models. Marcel  Dekker.  
• Seber GAF & Wild CJ. 1989. Non-linear Regression. John Wiley.  

 

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SURVIVAL ANALYSIS

Objective  

• The course deals with the study of demographic profiles and survival times.  In-depth  statistical  properties  and  analysis  is  an  important  component  of  this course.  

 

Theory 

• UNIT I
• Measures  of  Mortality  and  Morbidity:  Ratios  and  proportions,  rates  of  continuous  process,  rates  of  repetitive  events  ,crude  birth  rate,  Mortality  measures  used  in  vital  statistics  relationships  between  crude  and  age  specific  rates,  standardized  mortality  ratios  ,evaluation  of  person-year  of  exposed to risk in long term studies, prevalence and incidence of a disease,  relative risk and odds ratio.  
• Survival  Distribution:  Survival  functions,  hazard  rate,  hazard  function,  review  of  survival  distributions:  exponential,  Weibull,  Gamma,  Rayleigh,  Pareto,  Lognormal~  IFR  and  TFRA,  Gompertz  and  Makeham.  Gompertz  and    logistic    distributions.    Parametric    (m.l.e)    estimation.    Types    of  Censoring: Type I, Type II, random and other types of censoring, right and  left  truncated  distributions.  Expectation  and  variance  of  future  life  time,  series and parallel system of failures.  
• Life Tables: Fundamental and construction.  
• UNIT II
• Complete  Mortality  data,  Estimation  of  Survival  Function  :  Empirical  survival function , estimation of survival function from grouped mortality  data,   joint   distribution   of   the   number   of   deaths,   distribution   of   the  estimation  P i  covariance  of  estimate,  estimation  of  curves  of  deaths  and  central death rate and force of mortality rate .  
• Incomplete  Mortality   data  (non-parametric   models):  Actuarial  method,  m.1.e method, moment and reduced sample method of estimation and their  comparison.  Product  limit  (Kaplan-Meier)  method  and  cumulative  hazard  function (CHF) of estimation of survival function.  
• UNIT III
• Fitting Parametric Survival Distribution : Special form of survival function  cumulative  hazard  function  (CHF)  plots,  Nelson's  method  of  ungrouped  data, construction of the likelihood function for survival data, least squares  fitting, fitting a Gompertz distribution to grouped data.  
• Some  tests  of  Goodness  of  fit:  Graphical,  Kolmogorov-Smirnov  statistics  for complete, censored and truncated data, Chi-Square test and Anderson-  Darling A -statistics.  
• Comparison of Mortality Experiences: Comparison of two life tables, some  distribution- free methods (two samples) for ungrouped data, Two samples  Kolmogorov-Smirnov  test,  Wilcoxon  test  for  complete  data  and  modified  Wilcoxon  test  for  incomplete  data  .Gilbert  and  Gehan's  test,  mean  and  variance of Wilcoxon statistics, generalization of Gehan's test. Testing for  Consistent  Differences  in  Mortality  :  Mantel-Haenszel  and  log  rank  test.  Generalized Mantel-Haenszel test (k-sample).  
• UNIT IV
• Concomitant Variables: General parametric model for hazard function with  observed  concomitant  variables.  Additive  and  multiplicative  models  of  hazard   rate   functions.   Estimating   multiplicative   models,   selection   of  concomitant   variables.   Logistic   linear   model,   Concomitant   Variable  regarded  as  random variable.  Age  of  onset  distributions:  Models  of  onset  distributions and their estimation.  
• Gompertz distribution, parallel system and Weibull distribution, Fatal short  models of failure. Two component series system.  

 

Suggested Readings 

• Anderson B. 1990. Methodological Errors in Medical Research. Blackwell.  
• Armitage  P  &  Berry  G.  1987.  Statistical  Methods  in  Medical  Research.  Blackwell.  
• Collett D. 2003. Modeling Survival Data in Medical Research. Chapman &  Hall.  
• Cox DR  & Oakes D. 1984. Analysis of Survival Data. Chapman &  Hall.  
• Elandt-Johnson  RC  &  Johnson  NL.  1980.  Survival  Models  and  Data Analysis. John Wiley.  
• Everitt BS & Dunn G. 1998.  Statistical Analysis of Medical Data. Arnold.  
• Hosmer   DW   Jr.   &   Lemeshow   S.   1999.   Applied   Survival   Analysis: 
• Regression Modeling or Time to Event. John Wiley.  
• Kalbfleisch  JD  &  Prentice.  RL  2002.  The  Statistical  Analysis  of  Failure Time Data. John Wiley.  
• Klein  JP  &  Moeschberger  ML.  2003.  Survival  Analysis:  Techniques  for Censored and Truncated Data. Springer.  
• Kleinbaum DG & Klein M. 2002. Logistic Regression. Springer.  
• Kleinbaum DG & Klein M. 2005. Survival Analysis. Springer.  
• Lawless  JF.  2003.  Statistical  Models  and  Methods  for  Lifetime  Data.  2  nd  Ed. John Wiley.  
• Lee  ET.  1980.  Statistical  Methods  for  Survival  Data  Analysis.  Lifetime  Learning Publ.  

 

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ADVANCED BIOINFORMATICS

Objective  

• This  is  a  course  on  Bioinformatics  that  aims  at  exposing  the  students  to  some   advanced   statistical   and   computational   techniques   related   to  bioinformatics.    This course would  prepare the  students in understanding  bioinformatics principles and their applications.  

 

Theory 

• UNIT I
• Genomic  databases  and  analysis  of  high-throughput  data  sets,  sequence  annotation,   ESTs,   SNPs.   BLAST   and   related   sequence   comparison  methods. EM algorithm and other statistical methods to discover common  motifs in biosequences. Multiple alignment and database search using motif  models,  ClustalW  and  others.  Concepts  in  phylogeny.  Gene  prediction  based on codons, Decision trees, Classificatory analysis, Neural Networks,  Genetic algorithms, Pattern recognition, Hidden Markov models.  
• UNIT II
• Computational   analysis   of   protein   sequence,   structure   and   function.  Expression  profiling  by  microarray/gene  chip,  proteomics  etc.,  Multiple  alignment  of  protein  sequences,  Modelling  and  prediction  of  structure  of  proteins, Designer proteins, Drug designing.  
• UNIT III
• Analysis  of  one  DNA  sequence  (Modeling  signals  in  DNA;  Analysis  of  patterns;  Overlaps  and  Generalizations),  Analysis  of  multiple  DNA  or  protein sequences (Alignment algorithms - Gapped global comparisons and  Dynamic  programming;  use  of  linear  gap  models;  protein  sequences  and  substitution  matrices  -  BLOSUM,  PAM;  Multiple  sequences),  BLAST  (Comparison of two aligned sequences - Parameter calculation; Choice of a  score;  Bounds  for  P-value;  Normalized  and  Bit  scores,  Karlin  -  Altschul  sum    statistic;    comparison    of    two    unaligned    sequences;    Minimum  significance Lengths).  
• UNIT IV
• Markov   chains   (MC   with   no   absorbing   states;   Higher   order   Markov  dependence; patterns in sequences; Markov chain Monte Carlo - Hastings-  Metropolis  algorithm,  Gibbs  sampling,  Simulated  Annealing;  MC  with  absorbing   States,   Continuous-Time   Markov   chains)   Hidden   Markov  Models  (Forward and Backward algorithm; Viterbi algorithms; Estimation  algorithm;  
• UNIT V
• Modeling  protein  families;  Multiple  sequence  alignments;  Pfam;  Gene  finding),    Computationally    intensive    methods    (Classical    estimation  methods;   Bootstrap   estimation   and   Confidence   Intervals;   Hypothesis  testing;  Multiple  Hypothesis  testing),  Evolutionary  models  (Models  of  Nucleotide  substitution;  Discrete time  models  - The Jukes-Cantor Model,  
• The Kimura Model, The Felsenstein Model; Continuous-time models),  
• UNIT VI
• Phylogenetic tree estimation (Distances; Tree reconstruction - Ultrametric  and   Neighbor-Joining   cases;   Surrogate   distances;   Tree   reconstruction;  Parsimony    and    Maximum    Likelihood;    Modeling,    Estimation    and  
• Hypothesis Testing;)  Neural  Networks  (Universal  Approximation  Properties;  Priors  and Likelihoods, Learning  Algorithms      -  Backpropagation; Sequence encoding and output interpretation; Prediction  of  Protein  Secondary  Structure;  Prediction  of  Signal  Peptides  and  their  cleavage  sites;  Application  for  DNA  and  RNA  Nucleotide  Sequences),  Analysis of SNPs and Haplotypes.  

 

Suggested Readings 

• Baldi   P   &   Brunak   S.   2001.   Bioinformatics:   The   Machine   Learning Approach. MIT Press.  
• Baxevanis  AD  &  Francis  BF.  (Eds.).  2004.  Bioinformatics:  A  Practical Guide to the Analysis of Genes and Proteins. John Wiley.  
• Duda RO, Hart PE & Stork DG. 1999. Pattern Classification. John Wiley.  
• Ewens  WJ  &  Grant  GR.  2001.  Statistical  Methods  in  Bioinformatics.  Springer.  
• Jones NC & Pevzner PA. 2004. Introduction to Bioinformatics Algorithims.  The MIT Press.  
• Koskinen T. 2001. Hidden Markov Models for Bioinformatics. Kluwer.  
• Krane DE & Raymer ML. 2002. Fundamental Concepts of Bio-informatics.  Benjamin / Cummings.  
• Krawetz  SA  &  Womble  DD.  2003.  Introduction  to  Bioinformatics:  A Theoretical and Practical Approach. Humana Press.  
• Lesk AM. 2002. Introduction to Bio-informatics. Oxford Univ. Press.  
• Linder E &  Seefeld K. 2005. R for Bioinformatics. O'Reilly & Associates.  Percus  JK.  2001.  Mathematics  of  Genome  Analysis.  Cambridge  Univ.  Press.  
• Sorensen   D   &   Gianola   D.   2002.  Likelihood,   Bayesian   and   MCMC  Methods in Genetics. Springer.  
• Tisdall   JD.   2001.   Mastering   Perl   for   Bioinformatics.   O'Reilly   &  Associates.  
• Wang  JTL,  Zaki  MJ,  Toivonen  HTT  &  Shasha  D.  2004.  Data  Mining  in Bioinformatics. Springer.  
• Wu CH & McLarty JW. 2000. Neural Networks and Genome Informatics.  Elsevier.  
• Wunschiers R. 2004. Computational Biology Unix/Linux, Data Processing and Programming. Springer.  
• Yang MCC. 2000. Introduction to Statistical Methods in Modern Genetics.  
• Taylor & Francis.  

 

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ADVANCED ECONOMETRICS

Objective  

• This is a course on Econometrics  aims at exposing the students to  some  advanced level econometric methods and their applications to agricultural  situations.  

 

Theory 

• UNIT I
• Quantile  regression,  binary  quantile  regression,  extreme  values,  copula,  loss functions, Point and interval forecasting, unconditional and conditional  forecasting,    forecasting    with    serially    correlated    errors,    bootstrap:  asymptotic expansion, bootstrap consistency, asymptotic refinement, recent  developments for dependent time series  
• UNIT II
• Multivariate  time  series:  modelling  the  mean,  stationary  VAR  models:  properties, estimation, analysis and forecasting, VAR models with elements  of    nonlinearity,    Non-stationary    multivariate    time    series:    spurious  regression,   co-integration,   common   trends;   Volatility:   Modelling   the  variance, The class of ARCH models: properties, estimation, analysis and  forecasting, stochastic volatility, realized volatility.  
• UNIT III
• Basic Concepts of Bayesian Inference, Probability and Inference, Posterior  Distributions and Inference, Prior Distributions. The Bayesian linear model  and   autoregressive   (AR)   processes;   Model   selection   with   marginal  likelihoods  and  fractional  priors,  Comparison  of  Bayesian  Methods  with  Classical   approaches,   Bayes   risk   and   their   applications,   and   Sample  Selection   Monte   Carlo   integration,   importance   sampling   and   Gibbs  sampling,  The  Regression  Model  with  General  Error  Covariance  Matrix,  Qualitative Choice Models, Bayesian information criterion (BIC), Markov  Chain  Monte  Carlo  (MCMC)  Model  Composition  and  stochastic  search  variable  selection,  BUGS  [Bayesian  Inference  Using  Gibbs  Sampling]  ,  BUCC [Bayesian Analysis, Computation and Communication].  Technometrics 

 

Suggested Readings  

• Banerjee  A,  Dolado  J,  Galbraith  J  &  Hendry  DF.   1993.  Co-integration, 
• Error Correction, and the Econometric Analysis of   Nonstationary Data. Oxford Univ. Press. 
• Bauwens  L,  Lubrano   M  &  Richard  JF.  1999.  Bayesian  Inference  in Dynamics of Econometric Models. Oxford Univ. Press. 
• Carlin  BP  &  Louis  TA.  1996.  Bayes  and  Empirical  Bayes  Methods  for Data Analysis. Chapman & Hall. 
• Gilks  WR,  Richardson  S  &  Spiegelhalter  D.  1996.  MCMC  in  Practice. Chapman & Hall. 
• Greenberg  E.  2008.  Introduction  to  Bayesian  Econometrics.  Cambridge Univ. Press. 
• Hamilton JD. 1994. Time Series Analysis. Princeton Univ. Press. 
• Judge  GG,  Griffith  WE,  Hill  RC,  Lee  CH  &  Lutkepohl  H.  1985.  The Theory and Practice of Econometrics. 2   Ed. John Wiley. 
• Koop  G,  Poirier  D  &  Tobias  J.  2007.  Bayesian  Econometric  Methods. Cambridge Univ. Press. 
• Koop G. 2003. Bayesian Econometrics. John Wiley. 
• Lancaster  A.  2004.    An  Introduction  to  Modern  Bayesian  Econometrics. Blackwell. 
• Pindyck  RS  &  Rubinfeld  DL.  1981.  Econometric  Models  and  Economic Forecasts. McGraw Hill. 

 

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RECENT ADVANCES IN THE FIELD OF SPECIALIZATION  

Objective  

• To  familiarize  the  students  with  the  recent  advances  in  the  areas  of  their  specialization to prepare them for undertaking research.  
• Theory 
• Recent advances in the field of specialization - sample surveys / design of  experiments  /statistical  genetics  /  statistical  modeling  /  econometrics  /  statistical  inference,  etc.  will  be  covered  by  various  speakers  from  the  University / Institute as well as from outside the University / Institute in the  form of seminar talks.  

 

List of Journals

Agricultural Statistics  

• American Statistician 
• Annals of Institute of Statistical Mathematics 
• Annals of Statistics 
• Australian and New Zealand Journal of Statistics 
• Biometrical Journal 
• Biometrics 
• Biometrika 
• Bulletin of Calcutta Statistical Association 
• Canadian Journal of Statistics 
• Communication in Statistics (Simulation & Computation) 
• Communication in Statistics ( Theory & and Methods) 
• Experimental Agriculture 
• Institute of Mathematical Statistics Bulletin (IMSB) 
• Journal of American Statistical Association 
• Journal of Applied Statistics 
• Journal of the Indian Society of Agricultural Statistics 
• Journal of the International Statistical Review 
• Journal of Statistical Planning and Inference 
• Journal of Statistical Theory and Practice 
• Journal of Statistics, Computer and Applications 
• Journal of Royal Statistical Society, Series A 
• Journal of Royal Statistical Society, Series B 
• Journal of Royal Statistical Society, Series C 
• Metrika 
• Metron 
• Scandinavian Journal of Statistics (Theory & Applied) 
• Sankhya 
• Statistica 
• Statistical Science 
• Statistics and Probability Letters  
• Technometrics 

 

Computer Application  

• ACM Transactions on Knowledge Discovery from Data 
• Applied Intelligence - The International Journal of Artificial Intelligence, Neural Networks, and Complex Problem-Solving Technologies 
• Computational Statistics & Data Analysis, Elsevier Inc. 
• Computers and Electronics in Agriculture, Elsevier Inc. 
• Data Mining and Knowledge Discovery: An International Journal (DMKD) 
• Expert Systems with Applications, Elsevier Inc. 
• IEEE Transactions on Knowledge and Data Engineering 
• IEEE Transactions on Neural Networks
• IEEE Transactions on Pattern Analysis and Machine Intelligence 
• International Journal of Computing and Information Sciences 
• International Journal of Information and Management Sciences 
• International Journal of Information Technology 
• Journal of Artificial Intelligence Research 
• Journal of Combinatorics, Information and System Sciences 
• Journal of Computer Sciences and Technology 
• Journal of Computer Society of India 
• Journal of Indian Society of Agricultural Statistics 
• Journal of Intelligent Information Systems - Integrating Artificial Intelligence and Database Technologies 
• Journal of Machine Learning Research 
• Journal of Statistics, Computer and Applications 
• Journal of Systems and Software 
• Journal of Theoretical and Applied Information Technology 
• Knowledge and Information Systems: An International Journal (KAIS) 
• Lecture Notes in Computer Science, Springer Verlag. 
• Machine Learning 
• Transactions on Rough Set 

 

e-Resources

• Design Resources Server. Indian Agricultural Statistics Research Institute(ICAR), New Delhi 110 012, India. www.iasri.res.in/design. 
• Design Resources: www.designtheory.org 
• Free Encyclopedia on Design of Experiments 
• http://en.wikipedia.org/wiki/Design_of_experiments 
• Statistics Glossary http://www.cas.lancs.ac.uk/glossary_v1.1/main.html. 
• Electronic Statistics Text Book: http://www.statsoft.com/textbook/stathome.html. 
• Hadamard Matrices http://www.research.att.com/~njas/hadamard; 
• Hadamard Matrices http://www.uow.edu.au/~jennie/WILLIAMSON/williamson.html. 
• Course on Experimental design: http://www.stat.sc.edu/~grego/courses/stat706/. 
• Learning Statistics: http://freestatistics.altervista.org/en/learning.php. 
• Free Statistical Softwares: http://freestatistics.altervista.org/en/stat.php. 
• Statistics Glossary http://www.cas.lancs.ac.uk/glossary_v1.1/main.html. 
• Statistical Calculators: http://www.graphpad.com/quickcalcs/index.cfm 
• SAS Online Doc 9.1.3: http://support.sas.com/onlinedoc/913/docMainpage.jsp 

 

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Suggested Broad Topics for Research 

Agricultural Statistics 

• Design and analysis of multi-response experiments 
• Design and analysis of micro-array experiments 
• Design and analysis of experiments for precision agriculture 
• Design and analysis of agroforestry experiments 
• Bayesian designing of experiments, Bayesian optimality and Bayesian analysis of experimental data 
• Computer aided search of efficient experimentaldesigns for various experimental settings 
• Fractional factorials including search designs, supersaturated designs, computer experiments, etc. 
• Statistical techniques in bioinformatics, biotechnology, microbiology, genomics, etc. 
• Optimality aspects and robustness of designs against several disturbances unde various experimental settings (single factor,  multi-factor, nested classifications, etc.) 
• Small area estimation 
• Computer intensive techniques in sample surveys 
• Analysis of survey data, regression analysis, categorical data analysis, analysis of complex survey data 
• Assessment and impact survey methodologies,valuation of natural resources, its degradation, depletion, etc. 
• Linear and non-linear modeling of biological and economical phenomena 
• Non-linear time series modeling 
• Non-linear stochastic modeling 
• Forecast models for both temporal and spatial data 
• Innovative applications of resampling techniques 
• Applications of remote sensing, GIS, ANN etc. in modeling various phenomena 
• Econometric models for risk, uncertainty,  insurance, market analysis, technical efficiency, policy planning, etc. 
• Statistical studies on value addition to crop produce 

 

Computer Application 

• Web solutions in agriculture 
• Decision Support/Expert Systems/Information Management Systems in Agriculture 
• Software for Statistical Data Analysis 
• Modelling and Simulation of Agricultural Systems 
• Application Software for GIS and Remote Sensing 
• Office Automation and Management System 

 

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