A statistical test for Nested Sampling algorithms

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...

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Bibliographic Details
Published in:Statistics and computing Vol. 26; no. 1-2; pp. 383 - 392
Main Author: Buchner, Johannes
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2016
Subjects:
Artificial Intelligence
Mathematics and Statistics
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
MCMC
Evidence
Bayesian inference
Test
Nested sampling
Marginal likelihood
ISSN:0960-3174, 1573-1375
Online Access:Get full text
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Summary: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.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-014-9512-y