Material for the course "Bayesian Data Analysis & Cognitive Modeling" held at the University of Tübingen during the spring term of 2017
The main programming language we use is R. The slides and notes that accompany the lecture will use it, and whenever homeworks require programming, you will use it too.
It is recommended to use RStudio, because it nicely integrates with Rmarkdown, which is what you should use for your homework assignments.
There will be a number of R packages that we will need. Most importantly, we will work in the tidyverse. More necessary packages will be mentioned as we go along.
We will use three programming languages specialized for the formulation and computation of probabilistic inference. These are: JAGS, Stan, and WebPPL. All have their respective strengths and weaknesses.
JAGS is a specialized programming language to describe probabilistic models and perform Bayesian inference for these. It efficiently computes samples from the posterior distribution. We will communicate with JAGS from within R, using packages runjags, R2jags or rjags. We will use JAGS as a starting point and explore some simple cognitive models with it.
Stan is, like JAGS, a specialized programming language to describe probabilistic models and perform Bayesian inference for these. It efficiently computes samples from the posterior distribution and performs some additional magic (variational Bayes, MLE, …). Stan is particularly powerful for the computation of hierarchical models and we will use it to explore Bayesian approaches to regression modeling. We will communicate with Stan from within R, using packages RStan and RStanArm.
WebPPL is a general purpose probabilistic programming language. We will use it for the exploration of some more complex cognitive models. We will communicate with WebPPL from within R, using package RWebPPL. WebPPL also has a browser-based interface, making it easy to explore simple probabilistic models very quickly.
A slick and accessible tool for Bayesian statistics is JASP. We will use it early on to adventure into the differences between classical and Bayesian approaches to hypothesis testing and inference.