integration with an adaptive harmonic mean algorithm

• DOI: 10.48550/arxiv.1808.08051
• Publication Date: 2020-08-30
• Authors: Allen Caldwell; Rafael C. Schick; Rafael C. Schick; Vasyl Hafych; Philipp Eller; Marco Szalay; Oliver Schulz
• Keywords: High Energy Physics - Experiment (hep-ex); Physics - Data Analysis, Statistics and Probability; FOS: Physical sciences; 0101 mathematics; Astrophysics - Instrumentation and Methods for Astrophysics; Instrumentation and Methods for Astrophysics (astro-ph.IM); 01 natural sciences; Data Analysis, Statistics and Probability (physics.data-an); ddc:; High Energy Physics - Experiment

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.