We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of "live points" varies to allocate samples more efficiently. In empirical tests the new method significantly improves calculation accuracy compared to standard nested sampling with the same number of samples; this increase in accuracy is equivalent to speeding up the computation by factors of up to ∼ 72 for parameter estimation and ∼ 7 for evidence calculations. We also show that the accuracy of both parameter estimation and evidence calculations can be improved simultaneously. In addition, unlike in standard nested sampling, more accurate results can be obtained by continuing the calculation for longer. Popular standard nested sampling implementations can be easily adapted to perform dynamic nested sampling, and several dynamic nested sampling software packages are now publicly available. 1

Sampling errors in nested sampling parameter estimation differ from those in Bayesian evidence calculation, but have been little studied in the literature. This paper provides the first explanation of the two main sources of sampling errors in nested sampling parameter estimation, and presents a new diagrammatic representation for the process. We find no current method can accurately measure the parameter estimation errors of a single nested sampling run, and propose a method for doing so using a new algorithm for dividing nested sampling runs. We empirically verify our conclusions and the accuracy of our new method.Comment: Very minor changes. 22 pages + appendix, 10 figures. Accepted by Bayesian Analysi

Nested sampling is an increasingly popular technique for Bayesian computation, in particular for multimodal, degenerate problems of moderate to high dimensionality. Without appropriate settings, however, nested sampling software may fail to explore such posteriors correctly; for example producing correlated samples or missing important modes. This paper introduces new diagnostic tests to assess the reliability both of parameter estimation and evidence calculations using nested sampling software, and demonstrates them empirically. We present two new diagnostic plots for nested sampling, and give practical advice for nested sampling software users in astronomy and beyond. Our diagnostic tests and diagrams are implemented in nestcheck: a publicly available 1 Python package for analysing nested sampling calculations, which is compatible with output from MultiNest, PolyChord and dyPolyChord.

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