Adaptive methods for sequential importance sampling with application to state space models

TL;DR

This paper introduces adaptive proposal strategies for particle filters in state space models, using criteria like the coefficient of variation to improve the quality of importance sampling.

Contribution

It presents new adaptive methods based on the coefficient of variation and chi-square distance to optimize proposal distributions in sequential Monte Carlo algorithms.

Findings

Coefficient of variation estimates chi-square distance effectively.

Proposed adaptive strategies improve particle filter performance.

Numerical example demonstrates practical benefits.

Abstract

In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms--also known as particle filters--relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus, we show how the long-used coefficient of variation of the weights can be used for estimating the chi-square distance between the target and instrumental distributions of the auxiliary particle filter. As a by-product of this analysis we obtain an auxiliary adjustment multiplier weight type for which this chi-square distance is minimal. Moreover, we establish an empirical estimate of linear complexity of the Kullback-Leibler divergence between the involved distributions. Guided by these results, we discuss adaptive designing of the particle filter proposal distribution and illustrate the methods on a numerical example.