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  Integration with an adaptive harmonic mean algorithm

Caldwell, A., Eller, P., Hafych, V., Schick, R., Schulz, O., & Szalay, M. (2020). Integration with an adaptive harmonic mean algorithm. International Journal of Modern Physics A, 35, 2050142. doi:10.1142/S0217751X20501420.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0008-1C0F-A Version Permalink: https://hdl.handle.net/21.11116/0000-0008-1C10-7
Genre: Journal Article

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 Creators:
Caldwell, Allen1, Author
Eller, Philipp1, Author
Hafych, Vasyl1, Author
Schick, Rafael1, Author
Schulz, Oliver1, Author
Szalay, Marco1, Author
Affiliations:
1Max Planck Institute for Physics, Max Planck Society and Cooperation Partners, ou_2253650              

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Free keywords: Statistical Methods
 Abstract: 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.

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 Dates: 2020
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: Other: MPP-2018-352
URI: https://publications.mppmu.mpg.de/?action=search&mpi=MPP-2018-352
arXiv: arxiv:1808.08051
DOI: 10.1142/S0217751X20501420
URI: https://inspirehep.net/literature/1691220
 Degree: -

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Title: International Journal of Modern Physics A
  Abbreviation : Int.J.Mod.Phys.A
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 35 Sequence Number: - Start / End Page: 2050142 Identifier: -