Integration with an Adaptive Harmonic Mean Algorithm
Abstract
Numerically estimating the integral of functions in high dimensional spaces is a non-trivial 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.
Cite
@article{arxiv.1808.08051,
title = {Integration with an Adaptive Harmonic Mean Algorithm},
author = {Allen Caldwell and Philipp Eller and Vasyl Hafych and Rafael C. Schick and Oliver Schulz and Marco Szalay},
journal= {arXiv preprint arXiv:1808.08051},
year = {2020}
}