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A statistical test for Nested Sampling algorithms

机译：嵌套抽样算法的统计测试

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摘要

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-understoodway, 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.
机译：嵌套采样是一种迭代集成过程，通过一次删除“活动”点来将先前的数据量缩小为更高的可能性。从一个不断增加的似然阈值之上的先验均匀地得出一个替换点。因此，在嵌套抽样中自然会出现从某个可能性值以上的空间抽取问题，这使得解决此问题的算法成为嵌套抽样框架的关键要素。如果绘制的点均匀分布，则点的删除会以易于理解的方式缩小体积，并且嵌套采样的集成不会产生偏差。在这项工作中，我开发了一个统计测试来检查是否是这种情况。此“收缩测试”对于在受控环境中验证嵌套采样算法很有用。我将收缩测试应用于测试问题，并表明由于过度优化，一些现有算法无法通过收缩测试。然后，我演示了可以构造一个简单的算法来解决此类问题。但是，与MULTINEST相比，该RADFRIENDS算法效率低下。

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