Grid Particle Gibbs with Ancestor Sampling for State-Space Models

TL;DR

This paper introduces a novel grid-based particle Gibbs with ancestor sampling algorithm that improves efficiency in Bayesian estimation of state-space models, especially in complex regime-switching scenarios.

Contribution

It proposes an innovative particle generation scheme using a deterministic grid on the state space, enhancing computational efficiency over existing methods.

Findings

Significant computational gains in challenging models

Effective sampling using approximate HMM representation

Improved performance in regime-switching models

Abstract

We consider the challenge of estimating the model parameters and latent states of general state-space models within a Bayesian framework. We extend the commonly applied particle Gibbs framework by proposing an efficient particle generation scheme for the latent states. The approach efficiently samples particles using an approximate hidden Markov model (HMM) representation of the general state-space model via a deterministic grid on the state space. We refer to the approach as the grid particle Gibbs with ancestor sampling algorithm. We discuss several computational and practical aspects of the algorithm in detail and highlight further computational adjustments that improve the efficiency of the algorithm. The efficiency of the approach is investigated via challenging regime-switching models, including a post-COVID tourism demand model, and we demonstrate substantial computational gains compared to previous particle Gibbs with ancestor sampling methods.