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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Matthias Troffaes

Troffaes, Matthias C. M., Krak, Thomas & Bains, Henna (2019), Two-State Imprecise Markov Chains for Statistical Modelling of Two-State Non-Markovian Processes, in Bock, Jasper De Campos, Cassio P. de Cooman, Gert de Quaeghebeur, Erik & Wheeler, Gregory eds, Proceedings of Machine Learning Research 103: ISIPTA'19. Ghent, PMLR, 394-403.

Author(s) from Durham

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