Course Description
Introduction to theory and methods of the Bayesian approach to statistical inference and data analysis. Covers components of Bayesian analysis (prior, likelihood, posterior), computational algorithms, and philosophical differences among various schools of statistical thought.
Additional Requirements for Graduate Students:
Additional and/or alternative problems of a more challenging
nature will be required for graduate students on homework
assignments and exams.
Athena Title
Applied Bayesian Statistics
Prerequisite
STAT 4510/6510 and STAT 4230/6230
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
The goal of this course is to provide a basic understanding of the philosophical, methodological, and computational underpinnings of the Bayesian approach to data analysis and inference. By the end of the course, students should be able to fully specify the components of a Bayesian model (likelihood, priors, hyperpriors) and carry out the requisite computations for the analysis of such a model. Students should also understand and be able to discuss the philosophical and practical differences between a Bayesian and classical data analysis and know when it is appropriate to use each. The course is aimed at students within the field of statistics as well as those in other disciplines who have interest and training in statistics, data analysis, and other quantitative methods.
Topical Outline
Historical introduction; basics of Bayesian analysis - likelihood, prior, posterior; model building and checking; sensitivity analysis; comparisons with frequentist approach (theoretical and practical); computing the posterior distribution; sampling from the posterior distribution; MCMC algorithms (Metropolis-Hasting algorithm, Gibbs sampler, modern methods).
Syllabus