Bayesian Posterior Repartitioning for Nested Sampling

Priors in Bayesian analyses often encode informative domain knowledge that can be useful making the inference process more efficient. Occasionally, however, priors may unrepresentative of parameter values for a given dataset, which result inefficient space exploration, or even incorrect inferences, particularly nested sampling (NS) algorithms. Simply broadening prior such cases inappropriate impossible some applications. Hence our previous solution to this problem, known as posterior repartitioning (PR), redefines and likelihood while keeping their product fixed, so inferences evidence estimates remain unchanged, but efficiency NS is significantly increased. In its most practical form, PR raises power β, introduced an auxiliary variable must determined on case-by-case basis, usually by lowering β from unity according pre-defined ‘annealing schedule’ until resulting converge consistent solution. Here we present very simple yet powerful alternative approach, instead treated hyperparameter inferred data alongside original parameters then marginalised over obtain final inference. We show through numerical examples (BPR) method provides robust, self-adapting computationally efficient ‘hands-off’ problem using NS. Moreover, unlike method, representative BPR has negligible computational overhead relative standard nesting sampling, suggests it should used default all analyses.