http://arxiv.org/abs/1908.04655
Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset, which can result in inefficient parameter space exploration, or even incorrect inferences, particularly for nested sampling (NS) algorithms. Simply broadening the prior in such cases may be inappropriate or impossible in some applications. Hence a previous solution of this problem, known as posterior repartitioning (PR), redefines the prior and likelihood 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. In its most practical form, PR raises the prior to some power $\beta$, which is introduced as an auxiliary variable that must be determined on a case-by-case basis, usually by lowering $\beta$ from unity according to some pre-defined
annealing schedule' until the resulting inferences converge to a consistent solution. We present here an alternative Bayesianautomated PR’ method, in which $\beta$ is instead treated as a hyperparameter that is inferred from the data alongside the original parameters of the problem, and then marginalised over to obtain the final inference. We show through numerical examples that this approach provides a robust and efficient `hands-off’ solution to addressing the issue of unrepresentative priors in Bayesian inference using NS. Moreover, we show that for problems with representative priors the method has a negligible computational overhead relative to standard nesting sampling, which suggests that it should be used in as a matter of course in all NS analyses.
X. Chen, F. Feroz and M. Hobson
Wed, 14 Aug 19
18/60
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