Enter marquis de Laplace In my first post on Bayesian data analysis, I did a brief overview of how Bayesian updating works using grid approximation to arrive at posterior distributions for our parameters of interest, such as a wide receiver’s catch rate. While the grid-based approach is simple and easy to follow, it’s just not practical. Before we turn to MCMC, in this post we’ll cover the popular approach known as Laplace approximation1, aka quadratic approximation.
First steps I was originally thinking of writing a blog post about multilevel models (aka hierachical, mixed, random effects) because of how useful they are for measuring player performance in sports1 (shameless self promotion for nflWAR here!). But the more I thought about it, the more I realized how ill-minded of an idea that was. Instead, I want to build up the intuition for how and why one would want to use a full Bayesian multilevel model.