Reed College · B.A. Mathematics · Math 392 · Mathematical Statistics · 2021 · Solo · course final
Poisson Regression, Three Ways
A mathematical-statistics final that fits a single Poisson GLM to library checkout counts three ways — maximum likelihood, ridge-penalized estimation, and full Bayesian inference via a hand-coded Metropolis MCMC sampler — and compares what each one says.
This final took a deliberately simple model — a Poisson generalized linear model for count data, fit to library book-checkout counts — and worked it through three different statistical philosophies to see where they agree and where they diverge.
The frequentist pass derives the likelihood, finds the maximum-likelihood estimates, and builds analytical confidence intervals. The penalized pass adds ridge regularization to watch how shrinkage moves the coefficients. The Bayesian pass specifies priors over the coefficients and samples the posterior with a hand-written Metropolis MCMC algorithm, then reads off credible intervals and posterior summaries.
Setting all three side by side is the whole point — a compact tour of how maximum likelihood, regularization, and Bayesian inference each frame the same uncertainty. The MCMC sampler and the Bayesian machinery here are exactly the tools that resurface in actuarial modeling.