A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions

TL;DR

This paper introduces the PRticle filter, a novel algorithm that enhances predictive recursion for nonparametric estimation of multivariate mixing distributions by using a particle filtering approach to efficiently approximate normalizing constants.

Contribution

The paper proposes the PRticle filter, combining predictive recursion with particle filtering, to improve nonparametric estimation in high-dimensional mixture models.

Findings

The PRticle filter converges reliably under certain conditions.

Simulation studies show improved accuracy over traditional methods.

Application to spatial data demonstrates practical effectiveness.

Abstract

Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration. When the support of the mixing distribution is of relatively low dimension, this is not a problem since quadrature methods can be used and are very efficient. But when the support is of higher dimension, quadrature methods are inefficient and there is no obvious Monte Carlo-based alternative. In this paper, we propose a new strategy, which we refer to as a PRticle filter, wherein we augment the basic PR algorithm with a filtering mechanism that adaptively reweights an initial set of particles along the updating sequence which are used to obtain Monte Carlo approximations of the normalizing constants. Convergence properties of the PRticle filter approximation are established and its empirical accuracy is demonstrated with simulation studies and a marked spatial point process data analysis.