Nested sampling estimates directly how the likelihood function relates to prior mass. The evidence (alternatively the marginal likelihood, marginal density of the data, or the prior predictive) is immediately obtained by summation. It is the prime result of the computation, and is accompanied by an estimate of numerical uncertainty. Samples from the posterior distribution are an optional byproduct, obtainable for any temperature. The method relies on sampling within a hard constraint on likelihood value, as opposed to the softened likelihood of annealing methods. Progress depends only on the shape of the "nested" contours of likelihood, and not on the likelihood values. This invariance (over monotonic relabelling) allows the method to deal with a class of phase-change problems which effectively defeat thermal annealing.

Maximum entropy is an optimal technique of image reconstruction, widely applicable in astronomy and elsewhere. We present a general-purpose algorithm, capable of generating maximum entropy images from a wide variety of types of data.

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