Bayesian inference for continuous-time hidden Markov models with an unknown number of states
Author(s)
Luo, Yu
Stephens, David A
Type
Journal Article
Abstract
We consider the modeling of data generated by a latent continuous-time Markov jump process with a state space of finite but unknown dimensions. Typically in such models, the number of states has to be pre-specified, and Bayesian inference for a fixed number of states has not been studied until recently. In addition, although approaches to address the problem for discrete-time models have been developed, no method has been successfully implemented for the continuous-time case. We focus on reversible jump Markov chain Monte Carlo which allows the trans-dimensional move among different numbers of states in order to perform Bayesian inference for the unknown number of states. Specifically, we propose an efficient split-combine move which can facilitate the exploration of the parameter space, and demonstrate that it can be implemented effectively at scale. Subsequently, we extend this algorithm to the context of model-based clustering, allowing numbers of states and clusters both determined during the analysis. The model formulation, inference methodology, and associated algorithm are illustrated by simulation studies. Finally, we apply this method to real data from a Canadian healthcare system in Quebec.
Date Issued
2021-09
Date Acceptance
2021-07-19
Citation
Statistics and Computing, 2021, 31 (5), pp.1-15
ISSN
0960-3174
Publisher
Springer Science and Business Media LLC
Start Page
1
End Page
15
Journal / Book Title
Statistics and Computing
Volume
31
Issue
5
Copyright Statement
© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://link.springer.com/article/10.1007%2Fs11222-021-10032-8
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Theory & Methods
Statistics & Probability
Computer Science
Mathematics
Bayesian model selection
Continuous-time processes
Hidden Markov models
Markov chain Monte Carlo
Reversible jump algorithms
Model-based clustering
MONTE-CARLO METHODS
REVERSIBLE JUMP
MIXTURE-MODELS
PROGRESSION
Bayesian model selection
Continuous-time processes
Hidden Markov models
Markov chain Monte Carlo
Model-based clustering
Reversible jump algorithms
Statistics & Probability
0104 Statistics
0802 Computation Theory and Mathematics
Publication Status
Published
Article Number
57
Date Publish Online
2021-08-10