Statistics 385

Bayesian Analysis



Gelman and Hill, 2007



Data Analysis Using Regression and Multilevel/Hierarchical Models, 1st Edition (Amazon),
by Andrew Gelman and Jennifer Hill,
Cambridge, 2007
The following notes resulted from using RStudio, R, rstan, ggplot2, and knitr to explore the stan models kindly made available to all of us on github. Almost all of the R code and stan models originated from that source, but then sometimes morphed into late night minor explorations, as in musical ''variations on a theme.''

Resources


2. Concepts and methods from basic probability and statistics



Part 1A: Single-level regression

3. Linear regression: the basics

4. Linear regression: before and after fitting the model

5. Logistic regression

6. Generalized linear models



Part 1B: Working with regression inferences

7. Simulation of probability models and statistical inferences

8. Simulation for checking statistical procedures and model fits



9 Causal inference using regression on the treatment variable




McElreath, 2016



Statistical Rethinking, A Bayesian Course with Examples in R and Stan,
by Richard McElreath,
CRC Press, 2016

Preface

1. The Golem of Prague

2. Small Worlds and Large Worlds

3. Sampling the Imaginary

4. Linear Models

5. Multivariate Linear Models

6. Overfitting and Model Comparison

7. Interactions

8. Markov chain Monte Carlo Estimation

9. Big Entropy and the Generalized Linear Model

10. Counting and Classification

11. Monsters and Mixtures

12. Multilevel Models

13. Adventures in Covariance

14. Missing Data and Other Opportunities

15. Horoscopes




Hoff, 2009



A First Course in Bayesian Statistical Methods,
by Peter Hoff,
Springer, 2009

Resources



Kéry and Schaub, 2012



Bayesian population analysis using WinBUGS, A hierarchical perspective,
by Marc Kéry and Michael Schaub,
Academic Press, 2012

Resources


1. Introduction

2. Brief introduction to Bayesian statistical modeling

3. Introduction to the generalized linear model (GLM): The simplest model for count data


4. Introduction to random effects: Conventional Poisson GLMM for count data.



Gelman, et al., 2014



Bayesian Data Analysis, Third Edition,
by Andrew Gelman, et al.,
CRC Press, 2014

tutorial

Stan models

Stan, RStan, bayesplot, ShinyStan





cparrish@sewanee.edu