https://github.com/zhangry868/Bayesian-Statistics

Course material for Bayesian and Modern Statistics, STA601, Duke University, Spring 2015.
https://github.com/zhangry868/Bayesian-Statistics

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

• Host: GitHub
• URL: https://github.com/zhangry868/Bayesian-Statistics
• Owner: zhangry868
• License: other
• Created: 2016-10-28T19:54:25.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2016-03-09T17:16:21.000Z (over 8 years ago)
• Last Synced: 2024-05-22T19:35:47.969Z (5 months ago)
• Language: TeX
• Size: 55.8 MB
• Stars: 20
• Watchers: 2
• Forks: 27
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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• awesome-bayesian-statistics - STA360/601 - Bayesian Inference and Modern Statistical Methods, Duke University

README

        
# 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.