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

Area of Science:

• Computational Statistics
• Epidemiology
• Bioinformatics

Background:

• Bayesian inference for coupled hidden Markov models often uses data augmentation for hidden state imputation.
• Markov chain Monte Carlo (MCMC) methods are common but can be inefficient for high-dimensional or complex hidden processes due to autocorrelation or computational intractability.

Purpose of the Study:

• To develop a novel MCMC algorithm that balances computational efficiency and good mixing properties for analyzing complex hidden Markov models.
• To provide a method suitable for models with a large number of hidden chains, including relaxed Markovian assumptions.

Main Methods:

• A modified forward filtering backward sampling algorithm was developed as a novel MCMC approach.
• The algorithm is designed to handle increased dimensionality and complexity of hidden processes more efficiently than existing methods.

Main Results:

• The novel MCMC algorithm achieves a favorable balance between computation and mixing properties.
• Demonstrated applicability to models with large numbers of hidden chains and potential relaxation of Markovian assumptions.

Conclusions:

• The developed MCMC algorithm offers an efficient solution for Bayesian inference in complex hidden Markov models.
• The method is particularly advantageous for analyzing epidemic models, such as tracking *Escherichia coli* O157:H7 spread in cattle.