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The statistical evidence (or marginal likelihood) is a key quantity inBayesian statistics, allowing one to assess the probability of the data giventhe model under investigation. This paper focuses on refining the powerposterior approach to improve estimation of the evidence. The power posteriormethod involves transitioning from the prior to the posterior by powering thelikelihood by an inverse temperature. In common with other temperingalgorithms, the power posterior involves some degree of tuning. The maincontributions of this article are twofold -- we present a result from thenumerical analysis literature which can reduce the bias in the estimate of theevidence by addressing the error arising from numerically integrating acrossthe inverse temperatures. We also tackle the selection of the inversetemperature ladder, applying this approach additionally to the Stepping Stonesampler estimation of evidence.

Improving power posterior estimation of statistical evidence