Bayesian inference for spatio-temporal hidden Markov models using the exchange algorithm

2025-09-18

AI Summary

Spatial–temporal hidden Markov models (ST-HMMs) suffer from estimation challenges due to the intractability of the latent joint distribution, and conventional pseudo-likelihood methods introduce bias under strong latent variable dependencies. To address this, we propose a Bayesian ST-HMM incorporating an extended autologistic prior and embed the Approximate Exchange Algorithm within an MCMC framework—bypassing intractable normalizing constant computation. We further design a spatial neighborhood–informed initialization strategy to accelerate convergence and improve parameter estimation accuracy. Simulation studies demonstrate that our method substantially outperforms pseudo-likelihood estimation in terms of reduced parameter bias and superior posterior coverage robustness. Empirical analysis of regional rainfall data from Italy confirms the model’s practical effectiveness and interpretability in real-world spatiotemporal inference.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Spatio-temporal hidden Markov models are extremely difficult to estimate because their latent joint distributions are available only in trivial cases. In the estimation phase, these latent distributions are usually substituted with pseudo-distributions, which could affect the estimation results, in particular in the presence of strong dependence between the latent variables. In this work, we propose a spatio-temporal hidden Markov model where the latent process is an extension of the autologistic model. We show how inference can be carried out in a Bayesian framework using an approximate exchange algorithm, which circumvents the impractical calculations of the normalizing constants that arise in the model. Our proposed method leads to a Markov chain Monte Carlo sampler that targets the correct posterior distribution of the model and not a pseudo-posterior. In addition, we develop a new initialization approach for the approximate exchange method, reducing the computational time of the algorithm. An extensive simulation study shows that the approximate exchange algorithm generally outperforms the pseudo-distribution approach, yielding more accurate parameter estimates. Finally, the proposed methodology is applied to a real-world case study analyzing rainfall levels across Italian regions over time.

Problem

• Estimating spatio-temporal hidden Markov models with latent distributions
• Avoiding pseudo-distributions that bias results under dependence
• Developing Bayesian inference with exact posterior not pseudo-posterior

Innovation

• Bayesian inference with exchange algorithm
• Spatio-temporal hidden Markov model extension
• MCMC sampler targeting correct posterior distribution