Scalable Bayesian Inference for Coupled Hidden Markov and Semi-Markov Models

Panayiota Touloupou, Barbel Finkenstadt, Simon E. F. Spencer

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyze models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread of Escherichia coli O157:H7 in cattle. Supplementary materials for this article are available online.
Original languageEnglish
Pages (from-to)238-249
JournalJournal of Computational and Graphical Statistics
Issue number2
Publication statusPublished - 2 Apr 2020
Externally publishedYes


  • Coupled hidden Markov model
  • Data augmentation
  • Epidemics
  • Forward–backward algorithm
  • Markov chain Monte Carlo methods

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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