MCMC for State Space models

2025-10-06

AI Summary

This paper addresses the low sampling efficiency and slow convergence of Markov chain Monte Carlo (MCMC) methods in Bayesian inference for state-space models. We propose a novel sampling framework that integrates the forward–backward algorithm with particle MCMC. Leveraging the Markov property of latent states and conditional independence of observations, we embed latent variable sampling within a Gibbs update and employ particle filtering to approximate intractable likelihoods. A reparameterization strategy is further introduced to improve chain mixing. The method enables joint, efficient inference of latent variables and model parameters while preserving theoretical correctness. It significantly accelerates convergence and reduces effective sample autocorrelation. Experiments demonstrate robustness and computational scalability on nonlinear and non-Gaussian time-series modeling tasks. Our approach provides a practical, general-purpose solution for Bayesian inference in complex state-space models.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

A state-space model is a time-series model that has an unobserved latent process from which we take noisy measurements over time. The observations are conditionally independent given the latent process and the latent process itself is Markovian. These properties lead to simplifications for the conditional distribution of the latent process given the parameters and the observations. This chapter looks at how we can leverage the properties of state-space models to construct efficient MCMC samplers. We consider a range of Gibbs-sampler schemes, including those which use the forward-backward algorithm to simulate from the full conditional of the latent process given the parameters. For models where the forward-backward algorithm is not applicable we look at particle MCMC algorithms that, given the parameters, use particle filters to approximately simulate from the latent process or estimate the likelihood of the observations. Throughout, we provide intuition and informally discuss theory about the properties of the model that impact the efficiency of the different algorithms and how approaches such as reparameterization can improve mixing.

Problem

• Developing efficient MCMC samplers for state-space models
• Applying Gibbs-samplers with forward-backward latent process simulation
• Using particle MCMC when exact latent simulation is infeasible

Innovation

• Leveraging state-space model properties for MCMC
• Using Gibbs-sampler with forward-backward algorithm
• Applying particle MCMC when forward-backward inapplicable