Course

Unit I

Basics on minimaxity: subjective and frequents probability, Bayesian inference, Bayesian estimation , prior distributions, posterior distribution, loss function, principle of minimum expected posterior loss, quadratic and other common loss functions, Advantages of being a Bayesian HPD confidence intervals, testing, credible intervals, prediction of a future observation.

Unit II

Bayesian analysis with subjective prior, robustness and sensitivity, classes of priors, conjugate class, neighborhood class , density ratio class different methods of objective priors : Jeffrey’s prior, probability matching prior, conjugate priors and mixtures, posterior robustness: measures and techniques.

Unit III

Model selection and hypothesis testing based on objective probabilities and Bayes’ factors, large sample methods: limit of posterior distribution, consistency of posterior distribution, asymptotic normality of posterior distribution.

Unit IV

Bayesian Computations : analytic approximation, E- M Algorithm, Monte Carlo sampling, Markov Chain Monte Carlo Methods, Metropolis – Hastings Algorithm, Gibbs sampling, examples, convergence issues

CO1: To extend understanding of the practice of statistical inference.
CO2: To familiarize the student with the Bayesian approach to inference.
CO3:To describe computational implementation of Bayesian analyses.
CO4: Use Bayesian computational software, e.g. R, for realistically complex problems and interpret the results in context.

Text Book

1. Albert Jim (2009) Bayesian Computation with R, second edition, Springer, New York 2. Bolstad W. M. (2007) Introduction to Bayesian Statistics 2nd Ed. Wiley, New York

Reference Books

1. Christensen R. Johnson, W. Branscum A. and Hanson T.E. (2011) Bayesian Ideas and data analysis : A introduction for scientist and Statisticians, Chapman and Hall, London
2. Congdon P. (2006) Bayesian Statistical Modeling, Wiley , New York
3. Ghosh, J.K. Delampady M. and T. Samantha (2006). An Introduction to Bayesian Analysis : Theory and Methods, Springer, New York.
4. Lee P.M. (2004) Bayesian Statistics : An Introduction, Hodder Arnold, New York.