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Integration with an adaptive harmonic mean algorithm
International Journal of Modern Physics A ( IF 1.6 ) Pub Date : 2020-09-01 , DOI: 10.1142/s0217751x20501420
Allen Caldwell 1 , Philipp Eller 2 , Vasyl Hafych 1 , Rafael Schick 1, 2 , Oliver Schulz 1 , Marco Szalay 1
Affiliation  

Numerically estimating the integral of functions in high dimensional spaces is a nontrivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present an Adaptive Harmonic Mean Integration (AHMI) algorithm. Given samples drawn according to a probability distribution proportional to the function, the algorithm will estimate the integral of the function and the uncertainty of the estimate by applying a harmonic mean estimator to adaptively chosen regions of the parameter space. We describe the algorithm and its mathematical properties, and report the results using it on multiple test cases.

中文翻译:

与自适应调和平均算法集成

数值估计高维空间中函数的积分是一项不平凡的任务。一个经常遇到的例子是贝叶斯推理中边际似然的计算,在这种情况下,诸如马尔可夫链蒙特卡罗之类的采样算法提供了函数的样本。我们提出了一种自适应调和平均积分 (AHMI) 算法。给定根据与函数成比例的概率分布抽取的样本,该算法将通过将调和平均估计器应用于参数空间的自适应选择区域来估计函数的积分和估计的不确定性。我们描述了算法及其数学属性,并在多个测试用例上使用它报告了结果。
更新日期:2020-09-01
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