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Interest and application of Bayesian methods have exploded in recent decades, being facilitated by recent advances in computational power. Indeed, the Bayesian approach is now recognized across scientific disciples as a modern and powerful tool. We begin with an introduction to Bayes’ Theorem, the theoretical underpinning of Bayesian statistics which dates back to the 1700’s, and the concepts of prior and posterior distributions, conjugacy, and closed-form Bayesian inference. Building on this, we introduce modern computational approaches to performing Bayesian inference, including Markov chain Monte Carlo (MCMC), Metropolis-Hastings sampling, and the theory underlying these simple and powerful methods, before moving on to multivariate sampling methods and methodology. Students will become comfortable with modern software tools for MCMC using a variety of applied hierarchical modeling examples, and will use R for all statistical computing. The course will culminate in an independent Bayesian research project.
Grading: yes pass/fail option,
yes fifth course option
Homework, exams, and project
STAT 346, or permission of instructor
Juniors and Seniors, and Statistics majors
This course mandates significant mathematical and statistical prowess.