This repository collects supplementary materials for an applied course covering the essentials of Bayesian modeling from inference to computation. The goals of the course are to provide an overview of the basic aspects of analyzing scientific data within the Bayesian paradigm and to introduce modern computational tools for fitting and summarizing models. Each week, we will cover material that touches one one, or several, of the following:
- Bayesian inference and decision theory,
- linear and generalized linear models,
- hierarchical models,
- prior selection and model parameterization,
- model selection,
- model criticism, diagnostics, and visualization,
- Bayesian workflow,
- Markov chain Monte Carlo.
The material presented in this course will largely track with the Winter 2019 lectures by Richard McElreath (https://github.com/rmcelreath/statrethinking_winter2019). In broad strokes, the plan will be for participants in our class to watch two lectures per week, though at various points we may skip a few lectures or go through McElreath's course in a slightly different order. When we meet, we will review the main concepts covered in the online lectures and supplement the material with either worked examples, case studies, and additional mathematical/statistical details. Outlines of the material from our course will be posted in this repository along with links to references and additional readings.
Week 1: Introduction to Bayesian statistics
We will fit models using Stan, which provides a state of the art platform for Bayesian inference via Hamiltonian Monte Carlo. Installation instructions are available on the Stan website if you wish to explore Stan on your own machine. Many of the models we will touch on are can be fit off-the-shelf using the RStanArm and brms packages. We will also use the bayesplot package for visualization, and the LOO package for cross-validation.
Recommended books:
- Robert, Christian. The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. Springer Science & Business Media, 2007.
- Gelman, Andrew, et al. Bayesian Data Analysis. Chapman and Hall/CRC, 2013.
- Hoff, Peter D. A First Course in Bayesian Statistical Methods. Vol. 580. New York: Springer, 2009.
- Brooks, Steve, et al., eds. Handbook of Markov Chain Monte Carlo. CRC Press, 2011.
Additional resources:
- Stan forums: get help from the pros, when I have a question someone else has usually asked it first.
- Stan documentation: fantastic resource for all things Stan programming.
- Data methods discourse: thoughtful discourse on stats done right.
- Aki Vehtari's Bayes course: deeper, more mathematical presentation of what we'll cover. We'll borrow from this course as well.