Professor Matthias Troffaes matthias.troffaes@durham.ac.uk
Professor
Two-State Imprecise Markov Chains for Statistical Modelling of Two-State Non-Markovian Processes
Troffaes, Matthias C.M.; Krak, Thomas; Bains, Henna
Authors
Thomas Krak
Henna Bains
Contributors
Jasper De Bock
Editor
Cassio P. de Campos
Editor
Gert de Cooman
Editor
Erik Quaeghebeur
Editor
Gregory Wheeler
Editor
Abstract
This paper proposes a method for fitting a two-state imprecise Markov chain to time series data from a twostate non-Markovian process. Such non-Markovian processes are common in practical applications. We focus on how to fit modelling parameters based on data from a process where time to transition is not exponentially distributed, thereby violating the Markov assumption. We do so by first fitting a many-state (i.e. having more than two states) Markov chain to the data, through its associated phase-type distribution. Then, we lump the process to a two-state imprecise Markov chain. In practical applications, a two-state imprecise Markov chain might be more convenient than a many-state Markov chain, as we have closed analytic expressions for typical quantities of interest (including the lower and upper expectation of any function of the state at any point in time). A numerical example demonstrates how the entire inference process (fitting and prediction) can be done using Markov chain Monte Carlo, for a given set of prior distributions on the parameters. In particular, we numerically identify the set of posterior densities and posterior lower and upper expectations on all model parameters and predictive quantities. We compare our inferences under a range of sample sizes and model assumptions. Keywords: imprecise Markov chain, estimation, reliability, Markov assumption, MCMC
Citation
Troffaes, M. C., Krak, T., & Bains, H. (2019). Two-State Imprecise Markov Chains for Statistical Modelling of Two-State Non-Markovian Processes. In J. De Bock, C. P. de Campos, G. de Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), Proceedings of the Eleventh International Symposium on Imprecise Probabilities : Theories and Applications (394-403)
Conference Name | ISIPTA'19 |
---|---|
Conference Location | Ghent |
Acceptance Date | May 17, 2019 |
Publication Date | Jan 1, 2019 |
Deposit Date | Jun 17, 2019 |
Publicly Available Date | Mar 29, 2024 |
Pages | 394-403 |
Series Title | Proceedings of machine learning research |
Series Number | 103 |
Series ISSN | 2640-3498 |
Book Title | Proceedings of the Eleventh International Symposium on Imprecise Probabilities : Theories and Applications. |
Public URL | https://durham-repository.worktribe.com/output/1143961 |
Publisher URL | http://proceedings.mlr.press/v103/troffaes19b.html |
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Copyright Statement
This paper has been published under a Creative Commons Attribution 4.0 International License specified at http://creativecommons.org/licenses/by/4.0/legalcode (human
readable summary at http://creativecommons.org/licenses/by/4.0).
Published Conference Proceeding
(382 Kb)
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
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