Nested Sampling for Bayesian Computations
John Skilling · 2007
Abstract Nested sampling is a simple and general algorithm for directly computing the evidence Z (aka marginal likelihood) in multi-dimensional inference. It yields a Bayesian probability distribution Pr(Z) from which a central estimate and its uncertainty follow. Samples from the posterior distribution are available as a by-product with no extra computation. The method works by sampling proportionally to the prior, though constrained within a ‘nested’ sequence of progressively-higher likelihood contours. Exploration depends only on the shape of these contours and not on the associated values, so that nested sampling is invariant to monotonic re-labelling of likelihood. Thus, in multiphase applications, nested sampling bridges between different phases in a way denied to any thermal method, promising considerable extra scope. Although presented here in a Bayesian context, nested sampling is equally applicable to numerical integration of general positive functions in many dimensions.