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In real-world Bayesian inference applications, prior assumptions regardingthe parameters of interest may be unrepresentative of their actual values for agiven dataset. In particular, if the likelihood is concentrated far out in thewings of the assumed prior distribution, this can lead to extremely inefficientexploration of the resulting posterior by nested sampling algorithms, withunnecessarily high associated computational costs. Simple solutions such asbroadening the prior range in such cases might not be appropriate or possiblein real-world applications, for example when one wishes to assume a singlestandardised prior across the analysis of a large number of datasets for whichthe true values of the parameters of interest may vary. This work thereforeintroduces a posterior repartitioning (PR) method for nested samplingalgorithms, which addresses the problem by redefining the likelihood and priorwhile keeping their product fixed, so that the posterior inferences andevidence estimates remain unchanged but the efficiency of the nested samplingprocess is significantly increased. Numerical results show that the PR methodprovides a simple yet powerful refinement for nested sampling algorithms toaddress the issue of unrepresentative priors.

Improving the efficiency and robustness of nested sampling using posterior repartitioning