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We explore the arguments for maximizing the `evidence' as an algorithm formodel selection. We show, using a new definition of model complexity which weterm `flexibility', that maximizing the evidence should appeal to both Bayesianand Frequentist statisticians. This is due to flexibility's unique position inthe exact decomposition of log-evidence into log-fit minus flexibility. In theGaussian linear model, flexibility is asymptotically equal to the BayesianInformation Criterion (BIC) penalty, but we caution against using BIC in placeof flexibility for model selection.

The exact form of the 'Ockham factor' in model selection