Bayesian Information Criterion

Introduction
An alternative to Akaike Information Criterion (AIC) is the Bayesian Information Criterion, which is a slightly different setup to penalize using complex model families. We refer readers to well-written wikipedia pages BIC and AIC, and the references therein, for nice descriptions of these different formulations. The goal of my page here is to provide a local geometric view of the problem, which hopefully can be easier to understand.