**Description:** |
This course continues the development of Mathematical Statistics, with an emphasis on Bayesian analysis and underlying principles of inference. Topics include Bayesian Inference and Computation, Frequentist Inference and interpretation of p values and confidence intervals, Decision theory, admissibility and Stein’s paradox, the Likelihood principle, Exchangeability and De Finetti’s theorem, hierarchical modelling, multiple comparisons and False Discovery Rates. The mathematical level will generally be at that of an easy advanced calculus course. We will assume familiarity with standard statistical distributions (e.g., Normal, Poisson, Binomial, Exponential), with the laws of probability, expectation, conditional expectation, etc, and exposure to common statistical concepts such as p values and confidence intervals. Familiarity with the R statistical language will be helpful. Concepts will be illustrated mainly by instructive “toy” examples, where calculations can be done by hand. However, we will also study more complex, practical applications of Bayesian statistics. Although some basic methods of computation will be discussed, the primary focus will be on concepts and not on computation. |