Contemporary Statistical Inference

4 credits · Graduate School

This course is the second in a two-course series on probability and statistical inference that introduces and explores the fundamental inferential framework for parameter estimation, testing hypotheses, and interval estimation. Students learn classical methods of inference (hypothesis testing), and paradigms of statistical inference (frequentist, Bayesian, likelihood) and their surrounding controversies. Topics include sufficiency, minimal sufficiency, exponential family, ancillarity, completeness, conditionality principle, Fisher’s information, Cramer-Rao inequality, hypothesis testing (likelihood ratio test, most powerful test, optimality, Neyman-Pearson lemma, inversion of test statistics), likelihood principle, law of likelihood, Bayesian posterior estimation, interval estimation (confidence intervals, support intervals, credible intervals), basic asymptotic and large sample theory, and maximum likelihood estimation. This course is open to biostatistics students only; for students in other programs, instructor permission is required to enroll. [4]