Bayesian Statistics
Course material for Bayesian Inference and Modern Statistical Methods, STA360/601, Duke University, Spring 2015.
Textbook
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
Topics covered
Foundations
Bayes’ theorem, Definitions & notation, Decision theory, Beta-Bernoulli model, Gamma-Exponential model, Gamma-Poisson model
Background and motivation
What is Bayesian inference? Why use Bayes? A brief history of statistics
Exponential families and conjugate priors
One-parameter exponential families, Natural/canonical form, Conjugate priors, Multi-parameter exponential families, Motivations for using exponential families
Univariate normal model
Normal with conjugate Normal-Gamma prior, Sensitivity to outliers
Conditional independence relationships
Graphical models, De Finetti's theorem, exchangeability
Monte Carlo approximation
Monte Carlo, rejection sampling, importance sampling
Gibbs sampling
Markov chain Monte Carlo (MCMC) with Gibbs sampling, Markov chain basics, MCMC diagnostics
Multivariate normal model
Normal distribution, Wishart distribution, Normal with Normal-Wishart prior
Linear regression
Linear regression, basis functions, regularized least-squares, Bayesian linear regression
Hierarchical models and group comparisons
Hierarchical models, comparing multiple groups
Bayesian hypothesis testing
Testing hypotheses, Model selection/inference, Variable selection in linear regression
Priors
Informative vs. non-informative, proper vs. improper, Jeffreys priors
Metropolis–Hastings MCMC
Metropolis algorithm, Metropolis–Hastings algorithm
Generalized linear models (GLMs)
GLMs and examples (logistic, probit, Poisson)
Licensing
See LICENSE.