A statistical test for Nested Sampling algorithms
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Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a “live” point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood threshold. Thus, the problem of drawing from a space above a certain likelihood value arises naturally in nested sampling, making algorithms that solve this problem a key ingredient to the nested sampling framework. If the drawn points are distributed uniformly, the removal of a point shrinks the volume in a well-understood way, and the integration of nested sampling is unbiased. In this work, I develop a statistical test to check whether this is the case. This “Shrinkage Test” is useful to verify nested sampling algorithms in a controlled environment. I apply the shrinkage test to a test-problem, and show that some existing algorithms fail to pass it due to over-optimisation. I then demonstrate that a simple algorithm can be constructed which is robust against this type of problem. This RADFRIENDS algorithm is, however, inefficient in comparison to MULTINEST.
KeywordsNested sampling MCMC Bayesian inference Evidence Test Marginal likelihood
I would like to thank Frederik Beaujean and Udo von Toussaint for reading the initial manuscript. I acknowledge funding through a doctoral stipend by the Max Planck Society. This manuscript has greatly benefited from the comments of the two anonymous referees, whom I would also like to thank. I acknowledge financial support through a Max Planck society stipend.
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