This is the first in a series of posts that I plan on writing as I learn how to apply Bayesian methods to different topics/problems that I find interesting. In this post I go over how to use the Bayesian bootstrap to get measure of uncertainty for an NFL quarterback's (QB) yards per pass attempt (YPA).

What is the Bayesian Bootstrap and how do we compute it?¶

Bootstrapping is a resampling technique that allows us to calculate the uncertainty for a given statistic of interest (e.g. mean, median, etc.). In the classical bootstrap we construct these measures of uncertainty by first creating multiple datasets, called bootstrap samples, by sampling with replacement from the original data. Then for each of these newly generated samples, we calculate the statistic of interest and end up with an approximation of its distribution.

Here is an example of the classical bootstrap being used to construct an interval around a regression line: