  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.
