Improving power posterior estimation of statistical evidence

Nial Friel, Merrilee Hurn, Jason Wyse

Research output: Contribution to journalArticle

24 Citations (Scopus)
105 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)709-723
Number of pages15
JournalStatistics and Computing
Volume24
Issue number5
Early online date14 May 2013
DOIs
Publication statusPublished - Sep 2014

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Ladders
Tempering
Bayesian Statistics
Marginal Likelihood
Temperature
Refining
Numerical analysis
Tuning
Innovation
Statistics
Numerical Analysis
Likelihood
Evidence
Costs
Estimate
Model
Marginal likelihood
Bayesian statistics

Cite this

Improving power posterior estimation of statistical evidence. / Friel, Nial; Hurn, Merrilee; Wyse, Jason.

In: Statistics and Computing, Vol. 24, No. 5, 09.2014, p. 709-723.

Research output: Contribution to journalArticle

Friel, Nial ; Hurn, Merrilee ; Wyse, Jason. / Improving power posterior estimation of statistical evidence. In: Statistics and Computing. 2014 ; Vol. 24, No. 5. pp. 709-723.
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