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Journal Article

Integration with an adaptive harmonic mean algorithm

MPS-Authors

Caldwell,  Allen
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Eller,  Philipp
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Hafych,  Vasyl
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Schick,  Rafael
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Schulz,  Oliver
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Szalay,  Marco
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

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Citation

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.


Cite as: https://hdl.handle.net/21.11116/0000-0008-1C0F-A
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.