Bayes factor

The Bayes factor is the ratio of the marginal likelihoods of two competing models given the same data. It is the central quantity in Bayesian model comparison, quantifying the relative evidence for one model over another. Unlike a p-value, which assumes one model is true, the Bayes factor compares models symmetrically. Computing it requires evaluating the marginal likelihood, an integral that automatically penalizes complexity. For complex models, this integral is often approximated via Laplace approximation or variational methods.