  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.
