Properties of Nested Sampling

Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is asymptotically Gaussian. We show that the asymptotic variance of the nested sampling approximation typically grows linearly with the dimension of the parameter. We discuss the applicability and efficiency of nested sampling in realistic problems, and we compare it with two current methods for computing marginal likelihood. We propose an extension that avoids resorting to Markov chain Monte Carlo to obtain the simulated points.