Bayesian information criterion

The Bayesian information criterion (BIC) is a model selection criterion derived from the Laplace approximation to the marginal likelihood. Introduced by Gideon Schwarz in 1978, it penalizes complexity more aggressively than AIC by charging each parameter with a cost proportional to log n, where n is the sample size. This stronger penalty makes BIC consistent for selecting the true model — but only when the true model is actually in the candidate set, an assumption that is almost never met in practice. BIC is therefore a Bayesian formula with a frequentist soul: it claims to find the truth, but it only works in a world where truth is already on the menu.\n\n