Course: Introduction to computational Bayesian methods using Stan
Where: FU University Berlin When: 25-29 March 2019 Instructor: Prof. Shravan Vasishth (http://www.ling.uni-potsdam.de/~vasishth/) Course website: https://www.physalia-courses.org/courses-workshops/course46/ Overview In recent years, Bayesian methods have come to be widely adopted in all areas of science. This is in large part due to the development of sophisticated software for probabilisic programming; a recent example is the astonishing computing capability afforded by the language Stan (mc-stan.org). However, the underlying theory needed to use this software sensibly is often inaccessible because end-users don't necessarily have the statistical and mathematical background to read the primary textbooks (such as Gelman et al's classic Bayesian data analysis, 3rd edition). In this course, we seek to cover this gap, by providing a relatively accessible and technically non-demanding introduction to the basic workflow for fitting different kinds of linear models using Stan. To illustrate the capability of Bayesian modeling, we will use the R package RStan and a powerful front-end R package for Stan called brms. Prerequisites We assume familiarity with R. Participants will benefit most if they have previously fit linear models and linear mixed models (using lme4) in R, in any scientific domain. No knowledge of calculus or linear algebra is assumed, but basic school level mathematics knowledge is assumed (this will be quickly revisited in class). Some examples: given some variables x,x1,x2; what is xa×xb; what is exp(x1)×exp(x2); what is log(exp(x)); what is log(x1×x2). Outcomes After completing this course, the participant will have become familiar with the foundations of Bayesian inference using Stan (RStan and brms), and will be able to fit a range of multiple regression models and hierarchical models, for normally distributed data, and for log-normal, poisson, multinomial, and binomially distributed data. They will know how to calibrate their models using prior and posterior predictive checks; they will be able to establish true and false discovery rates to validate discovery claims, and to carry out model comparison using cross-validation methods, and Bayes factors. As background reading, we recommend: - For beginning readers (the intended audience for this course): A Student's Guide to Bayesian Statistics, by Ben Lambert. See: https://www.amazon.co.uk/Students-Guide-Bayesian-Statistics/dp/1473916364 - For technically sophisticated readers (familiarity with calculus and linear algebra assumed): Michael Betancourt's writings and case studies. See: https://betanalpha.github.io/ Program Monday - Classes from 9:30 to 17:30 Foundations of Bayesian inference - Probability theory and Bayes-Price-Laplace's rule - Probability distributions - Understanding and eliciting priors - Analytical Bayes: Beta-Binomial, Poisson-Gamma, Normal-Normal Tuesday - Classes from 9:30 to 17:30 Computational Bayes - Generating prior predictive distributions using RStan and R - Fake-data simulation for model evaluation - Sampling methods: - Inverse sampling - Gibbs sampling - Random Walk Metropolis - Hamiltonian Monte Carlo Wednesday - Classes from 9:30 to 17:30 Bayesian Modeling with Stan and brms - Introduction to Stan syntax - Introduction to brms - Linear models using RStan and brms Thursday - Classes from 9:30 to 17:30 Regression modeling using Stan and brms - Generalized linear models - Model evaluation and calibration - Model comparison using LOO and Bayes factor Friday - Classes from 9:30 to 17:30 Model evaluation and comparison - Hierarchical linear models - Fake-data generation for hierarchical data - Posterior predictive checks - Some instructive case studies
