Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

TL;DR

This tutorial introduces the particle Metropolis-Hastings algorithm for parameter inference in nonlinear state-space models, providing a step-by-step implementation guide and practical examples in R.

Contribution

It offers a comprehensive, accessible tutorial with an accompanying R package for implementing PMH in nonlinear dynamical models, including practical solutions.

Findings

Successful inference in linear Gaussian models with synthetic data

Application to nonlinear stochastic volatility model with real data

Implementation guidance and intuition for PMH algorithm

Abstract

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.