A statistical test for Nested Sampling algorithms

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• 作者：Johannes Buchner
• 关键词：Nested sampling ; MCMC ; Bayesian inference ; Evidence ; Test ; Marginal likelihood
• 刊名：Statistics and Computing
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：26
• 期：1-2
• 页码：383-392
• 全文大小：1,230 KB
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  Skilling, J.: Nested sampling’s convergence. In: BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE ANDENGINEERING. The 29th International Workshop on Bayesian Inference andMaximum Entropy Methods in Science and Engineering, vol. 1193, pp. 277–291. AIP Publishing, New York (2009)
  Skilling, J.: Bayesian computation in big spaces-nested sampling and galilean monte carlo. AIP Conf. Proc. 1443(1), 145–156 (2012)CrossRef
  
• 作者单位：Johannes Buchner (1)
  
  1. Max Planck Institut für Extraterrestrische Physik, Giessenbachstrasse, 85748, Garching, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics Computing and Software
  Statistics
  Numeric Computing
  Mathematics
  Artificial Intelligence and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-1375

文摘

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. Keywords Nested sampling MCMC Bayesian inference Evidence Test Marginal likelihood