Improving the efficiency and robustness of nested sampling using posterior repartitioning

Xi Chen, Michael Hobson, Saptarshi Das, Paul Gelderblom

Research output: Contribution to journalArticlepeer-review

Abstract

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings of the assumed prior distribution, this can lead to extremely inefficient exploration of the resulting posterior by nested sampling (NS) algorithms, with unnecessarily high associated computational costs. Simple solutions such as broadening the prior range in such cases might not be appropriate or possible in real-world applications, for example when one wishes to assume a single standardised prior across the analysis of a large number of datasets for which the true values of the parameters of interest may vary. This work therefore introduces a posterior repartitioning (PR) method for NS algorithms, which addresses the problem by redefining the likelihood and prior while keeping their product fixed, so that the posterior inferences and evidence estimates remain unchanged but the efficiency of the NS process is significantly increased. Numerical results show that the PR method provides a simple yet powerful refinement for NS algorithms to address the issue of unrepresentative priors.

Original languageEnglish
Pages (from-to)835-850
Number of pages16
JournalStatistics and Computing
Volume29
Issue number4
Early online date19 Nov 2018
DOIs
Publication statusPublished - 15 Jul 2019

Keywords

  • Bayesian modelling
  • Nested sampling
  • Posterior repartitioning
  • Unrepresentative prior

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

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