STAT 850/442 Statistical Inference
Description
This course presents a rigorous theoretical treatment of statistical inference, offering a comparative analysis of frequentist and Bayesian paradigms. The curriculum explores several core areas of statistical theory, beginning with foundational concepts in Decision theory (Risk Function, Minimaxity Theorem) before moving into a comprehensive treatment of Bayesian inference (Posterior, Bayes Rules, Bayes Risk, Minimax Rules, James-Stein Estimator, Empirical Bayes, Hierarchical Bayesian, MCMC, Case Study). The course then transitions to focus heavily on Likelihood theory (Sufficient Statistic, Bartlett’s Identities, Cramér-Rao Lower Bound, Exponential Families) and the mechanics of MLE (Score, Fisher Information, Newton-Raphson Methods, Asymptotics of Maximum Likelihood Estimators, Alkeike Information Criteria, Deep Learning). Finally, we cover hypothesis testing and optimal point estimation through the lens of the Likelihood ratio test (Neyman-Pearson Lemma, Monotone Likelihood Test, Likelihood-based Tests) and UMVUE (Complete Statistic, Uniformly Minimum Variance Unbiased Estimators/Tests).
Prerequisite(s): STAT 342.
This course requires a strong command of multivariate calculus, alongside a rigorous foundation in intermediate probability theory including asymptotic theorey for probability. Students should also possess prior exposure to applied statistical methods and familiar with basic statistical concepts such as p-value and confidence internal.