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 within linguistics and psychology. No knowledge of calculus or linear algebra is assumed (but will be helpful to know), but basic school level mathematics knowledge is assumed (this will be quickly revisited in class).

Please install the following software before coming to the course

We will be using the software R,
and RStudio,
so make sure you install these on your computer.
You should also install the R package rstan; the R package brms.

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 lognormal 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. If there is time, we will discuss how to carry out model comparison using Bayes factors and k-fold cross validation.

Online interaction

We will use google groups and zoom. A link to the private group will be sent to participants.

For this part of the workshop besides rstan and brms, be sure to have the following packages installed (and loaded in your session):
MASS, dplyr, tidyr, purrr, readr, extraDistr,
ggplot2, brms, bayesplot, tictoc, gridExtra
The lectures correspond roughly to chapters 3, 4 and 5 of our
textbook in preparation