PARNI for importance sampling and density estimation
A. van Hameren
TL;DR
The paper introduces PARNI, a general-purpose tool for adaptive importance sampling and density estimation in Monte Carlo integration on [0,1)^D. It builds a flexible, multi-channel density from constant-density hyper-rectangular regions that is updated batch-by-batch via subdivision of the most influential channels, with options for variance-aware weighting and memory management. A binary-tree architecture enables fast density evaluation and point generation, and the implementation is provided in Fortran77 with routines that can be integrated into existing simulation codes. The approach also addresses error estimation concerns in adaptive schemes by separating the adaptation phase from the final integration phase and is demonstrated with an example involving a delta-like spike.
Abstract
We present an aid for importance sampling in Monte Carlo integration, which is of the general-purpose type in the sense that it in principle deals with any quadratically integrable integrand on a unit hyper-cube of arbitrary dimension. In contrast to most existing systems of this type, it does not ask for the integrand as an input variable, but provides a number of routines which can be plugged into a given Monte Carlo program in order to improve its efficiency "on the fly" while running. Due to the nature of its design, it can also be used for density estimation, i.e., for the analysis of data points coming from an external source.