Conditional particle filters with diffuse initial distributions

TL;DR

This paper introduces an auxiliary variable method to improve the efficiency of conditional particle filters when dealing with diffuse initial distributions, applicable to various models and with online adaptation.

Contribution

It proposes a generally applicable auxiliary variable approach for CPFs that handles diffuse initial distributions using reversible Markov transitions, with theoretical validation and practical testing.

Findings

Method works reliably with minimal user input.

Substantially better mixing than particle Gibbs algorithms.

Effective across different models including epidemic and volatility models.

Abstract

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random-walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use on-line adaptations within the methods. In the case of random-walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear-Gaussian random-walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification, and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.