http://arxiv.org/abs/1808.08051
Efficiently estimating the integral of functions in high dimensional spaces is a non-trivial task when an analytical solution cannot be calculated. A oft-encountered example is in the calculation of the marginal likelihood, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present the 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 subvolumes of the parameter space. We describe the algorithm and it’s mathematical properties, and report the results using it on multiple test cases of up to 20 dimensions.
A. Caldwell, R. Schick, O. Schulz, et. al.
Mon, 27 Aug 18
5/46
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