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Improving power posterior estimation of statistical evidence

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Abstract

The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach to improve estimation of the evidence. The power posterior method involves transitioning from the prior to the posterior by powering the likelihood by an inverse temperature. In common with other tempering algorithms, the power posterior involves some degree of tuning. The main contributions of this article are twofold—we present a result from the numerical analysis literature which can reduce the bias in the estimate of the evidence by addressing the error arising from numerically integrating across the inverse temperatures. We also tackle the selection of the inverse temperature ladder, applying this approach additionally to the Stepping Stone sampler estimation of evidence. A key practical point is that both of these innovations incur virtually no extra cost.

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Acknowledgements

Nial Friel’s research was supported by a Science Foundation Ireland Research Frontiers Program grant, 09/RFP/MTH2199. Jason Wyse’s research was supported through the STATICA project, a Principal Investigator program of Science Foundation Ireland, 08/IN.1/I1879. We are grateful to two anonymous reviewers whose comments on an earlier version have much improved this work.

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Authors and Affiliations

  1. School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Republic of Ireland

    Nial Friel

  2. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK

    Merrilee Hurn

  3. School of Computer Science and Statistics, Trinity College Dublin, College Green, Dublin 2, Republic of Ireland

    Jason Wyse

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  1. Nial Friel
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  2. Merrilee Hurn
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  3. Jason Wyse
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Correspondence to Merrilee Hurn.

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Friel, N., Hurn, M. & Wyse, J. Improving power posterior estimation of statistical evidence. Stat Comput 24, 709–723 (2014). https://doi.org/10.1007/s11222-013-9397-1

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  • DOI: https://doi.org/10.1007/s11222-013-9397-1

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