PARNI for importance sampling and density estimation

TL;DR

This paper introduces PARNI, a versatile importance sampling tool that enhances Monte Carlo integration efficiency and can also be used for density estimation without requiring the integrand as input.

Contribution

PARNI provides a general-purpose, plug-in importance sampling method that improves Monte Carlo integration and density estimation dynamically during execution.

Findings

Improves efficiency of Monte Carlo integration.

Can be used for density estimation from external data.

Operates without needing the integrand as an input.

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.