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The Bayesian method is noted to produce spuriously high posteriorprobabilities for phylogenetic trees in analysis of large datasets, but theprecise reasons for this over-confidence are unknown. In general, theperformance of Bayesian selection of misspecified models is poorly understood,even though this is of great scientific interest since models are never true inreal data analysis. Here we characterize the asymptotic behavior of Bayesianmodel selection and show that when the competing models are equally wrong,Bayesian model selection exhibits surprising and polarized behaviors in largedatasets, supporting one model with full force while rejecting the others. Ifone model is slightly less wrong than the other, the less wrong model willeventually win when the amount of data increases, but the method may becomeoverconfident before it becomes reliable. We suggest that this extreme behaviormay be a major factor for the spuriously high posterior probabilities forevolutionary trees. The philosophical implications of our results to theapplication of Bayesian model selection to evaluate opposing scientifichypotheses are yet to be explored, as are the behaviors of non-Bayesian methodsin similar situations.

The good, the bad, and the ugly: Bayesian model selection produces spurious posterior probabilities for phylogenetic trees