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<p>This paper presents an exact inference framework for Bayesian multiple change-point detection, bridging the flexibility of Semiparametric Hidden Markov Models (SPHMM) with efficient recursive filtering. By deriving the explicit Beta-Geometric run-length distribution induced by the semiparametric prior structure, we circumvent the need for approximate Markov Chain Monte Carlo (MCMC) sampling. This formulation enables the calculation of the exact marginal likelihood and the direct simulation of independent posterior samples. Additionally, we implement an Empirical Bayes procedure for automatic hyperparameter optimization. Extensive simulations and an application to well-log data demonstrate that the proposed method, aided by a dynamic pruning strategy, yields parsimonious segmentations with superior model evidence and computational speedups of orders of magnitude compared to standard Gibbs sampling approaches.</p>

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Efficient and exact Bayesian inference for Dirichlet process hidden Markov multiple change-point models

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Masoud Majidizadeh

摘要

This paper presents an exact inference framework for Bayesian multiple change-point detection, bridging the flexibility of Semiparametric Hidden Markov Models (SPHMM) with efficient recursive filtering. By deriving the explicit Beta-Geometric run-length distribution induced by the semiparametric prior structure, we circumvent the need for approximate Markov Chain Monte Carlo (MCMC) sampling. This formulation enables the calculation of the exact marginal likelihood and the direct simulation of independent posterior samples. Additionally, we implement an Empirical Bayes procedure for automatic hyperparameter optimization. Extensive simulations and an application to well-log data demonstrate that the proposed method, aided by a dynamic pruning strategy, yields parsimonious segmentations with superior model evidence and computational speedups of orders of magnitude compared to standard Gibbs sampling approaches.