Course material for Bayesian Inference and Modern Statistical Methods, STA360/601, Duke University, Spring 2015.

The first half of this course was based on my own lecture notes (Chapters 1-6, Lecture Notes on Bayesian Statistics, Jeffrey W. Miller, 2015).

For the second half of the course, we used A First Course in Bayesian Statistical Methods, Peter D. Hoff, 2009, New York: Springer. http://www.stat.washington.edu/people/pdhoff/book.php

Bayes’ theorem, Definitions & notation, Decision theory, Beta-Bernoulli model, Gamma-Exponential model, Gamma-Poisson model

What is Bayesian inference? Why use Bayes? A brief history of statistics

One-parameter exponential families, Natural/canonical form, Conjugate priors, Multi-parameter exponential families, Motivations for using exponential families

Normal with conjugate Normal-Gamma prior, Sensitivity to outliers

Graphical models, De Finetti's theorem, exchangeability

Monte Carlo, rejection sampling, importance sampling

Markov chain Monte Carlo (MCMC) with Gibbs sampling, Markov chain basics, MCMC diagnostics

Normal distribution, Wishart distribution, Normal with Normal-Wishart prior

Linear regression, basis functions, regularized least-squares, Bayesian linear regression

Hierarchical models, comparing multiple groups

Testing hypotheses, Model selection/inference, Variable selection in linear regression

Informative vs. non-informative, proper vs. improper, Jeffreys priors

Metropolis algorithm, Metropolis–Hastings algorithm

GLMs and examples (logistic, probit, Poisson)

See LICENSE.