Chapter 3 STAT 206B: Intermediate Bayesian Inference

This chapter contains past exam problems of STAT 206B: Intermediate Bayesian Inference. There are two textbooks used for this class, Robert (2007) and Berger (1985). A tentative syllabus is listed here.

• Interpretations of probability: Subjective, Classical, Frequentist; Elicitation and representation of beliefs and uncertainty through probability distributions; Likelihoods.

• Priors and Posteriors: Bayes Theorem; Choice of priors; Calculation of posteriors; Conjugate analysis; Predictive distributions; Jeffreys priors and improper priors.

• Decision theoretic approaches to statistical inference; Expected losses; Frequentist and Bayesian risk; Optimality of Bayesian procedures.

• Exchangeability; Exponential families.

• Monte Carlo integration; Importance sampling; Laplace approximations.

• Markov chain Monte Carlo: Gibbs and Metropolis-Hasting sampling; Estimation of posterior distributions via MCMC; Drawing inferences, making predictions; Basic MCMC diagnostics; Simple hierarchical modeling.

• Bayesian Inference: Point estimation; Estimation Error; Interval estimation; Hypothesis test- ing; Bayes factors.

• Interpretation of results: Understanding posterior uncertainty.

References

Berger, James. 1985. Statistical Decision Theory and Bayesian Analysis. 2nd ed. New York City, NY: Springer Texts in Statistics.

Robert, Christian. 2007. The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. 2nd ed. New York City, NY: Springer Texts in Statistics.