Marginal likelihood

The marginal likelihood (also called the evidence) is the probability of the observed data given a model, averaged over all possible parameter values weighted by their prior. It is the integral that drives Bayesian model comparison and gives the Bayes factor its automatic complexity penalty. Because it averages over the prior, the marginal likelihood is sensitive to prior specification — a property that makes it both principled and controversial. Approximate computation is often necessary, using methods such as Laplace approximation or MCMC.