PARNI for importance sampling and density estimation

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.