  We introduce a general Monte Carlo method based on Nested Sampling (NS), for
sampling complex probability distributions and estimating the normalising
constant. The method uses one or more particles, which explore a mixture of
nested probability distributions, each successive distribution occupying ~e^-1
times the enclosed prior mass of the previous distribution. While NS
technically requires independent generation of particles, Markov Chain Monte
Carlo (MCMC) exploration fits naturally into this technique. We illustrate the
new method on a test problem and find that it can achieve four times the
accuracy of classic MCMC-based Nested Sampling, for the same computational
effort; equivalent to a factor of 16 speedup. An additional benefit is that
more samples and a more accurate evidence value can be obtained simply by
continuing the run for longer, as in standard MCMC.
