Bayesian

I’ve seen a number of examples of MCMC algorithms, and while they’re all solid, a lot of them tend to be a bit too neat - they have a fairly simple model, a single predictor (maybe two), and not much else. This one is a good example, as it covers the theory in detail, but it’s using an obviously toy data set. So I decided to throw together a slightly more intricate example, highlighting a couple of issues and tricks worth noting for a handwritten implementation.

Note that this post is written under the assumption that the reader already has some knowledge about what MCMC is generally for and broadly how it works. This post is all R code (see here), with no JAGS or BUGS or such. The tidyverse, patchwork, and ISLR libraries are required – the former two for the plots, the latter for the data set used.

Bayesian statistics is centered on constructing certain assumptions about how the probability of an event is distributed, and then adjusting that belief as new information comes in. It can be more involved to construct a Bayesian model as opposed to the “look at many things in aggregate” approach used in frequentist statistics. But it has nice properties, and we’ll take a look at them in a real albeit fairly unimportant context: the Pokemon video games.