Usually the marginal likelihood cannot be computed analytically. Numerical approximations can often be obtained, but for practical purposes it has proved very useful, and quite sufficient, to employ an approximation of the marginal likelihood. This approximation has become known as the Bayesian information criterion, or BIC for short (Schwarz 1978, Raftery 1995). It turns out that this approximation shows remarkable similarities to the AIC:  \[ \text{BIC}[M] \; = \; - 2 \log P(s \mid h_{\hat{\theta}(s)}) + d \log n . \]  Here \(\hat{\theta}(s)\) is again the maximum likelihood estimate of the model, \(d = dim(M)\) the number of independent parameters, and \(n\) is the number of data points in the sample. The latter dependence is the only difference with the AIC, but a major difference in how the model evaluation may turn out.