A statistical test for Nested Sampling algorithms
Abstract
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 everincreasing 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 wellunderstood 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 testproblem, and show that some existing algorithms fail to pass it due to overoptimisation. 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.
 Publication:

Statistics and Computing
 Pub Date:
 January 2016
 DOI:
 10.1007/s112220149512y
 arXiv:
 arXiv:1407.5459
 Bibcode:
 2016S&C....26..383B
 Keywords:

 Statistics  Computation
 EPrint:
 11 pages, 7 figures. Published in Statistics and Computing, Springer, September 2014