JCK-1096 / Bayesian-Statistics

Course material for Bayesian and Modern Statistics, STA601, Duke University, Spring 2015.

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.