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ejhigson committed Sep 16, 2018
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# Summary

Nested sampling [@Skilling2006] is a popular numerical method for calculating Bayesian evidences and generating posterior samples given some likelihood and prior.
The initial development of the algorithm was targeted at evidence calculation, but implementations such as ``MultiNest`` [@Feroz2008; @Feroz2009; @Feroz2013] and ``PolyChord`` [@Handley2015a; @Handley2015b] are now used extensively for parameter estimation in scientific research - see for example [@DESCollaboration2017].
The initial development of the algorithm was targeted at evidence calculation, but implementations such as ``MultiNest`` [@Feroz2008; @Feroz2009; @Feroz2013] and ``PolyChord`` [@Handley2015a; @Handley2015b] are now used extensively for parameter estimation in scientific research - see for example [@Joudaki2016; @DESCollaboration2017; @Chua2018].
Nested sampling performs well compared to Markov chain Monte Carlo (MCMC)-based alternatives at exploring multimodal and degenerate distributions, and the ``PolyChord`` software is well-suited to high-dimensional problems.

Dynamic nested sampling [@Higson2017b] is a generalisation of the nested sampling algorithm which dynamically allocates samples to the regions of the posterior where they will have the greatest effect on calculation accuracy. This allows order-of-magnitude increases in computational efficiency, with the largest gains for high dimensional parameter estimation problems.
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