Home > Research > Publications & Outputs > Direct statistical inference for finite Markov ...

Electronic data

  • MatExp

    Accepted author manuscript, 405 KB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License


Text available via DOI:

View graph of relations

Direct statistical inference for finite Markov jump processes via the matrix exponential

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>31/12/2021
<mark>Journal</mark>Computational Statistics
Issue number4
Number of pages25
Pages (from-to)2863-2887
Publication StatusPublished
Early online date19/04/21
<mark>Original language</mark>English


Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, Q, since exp (Qt) is the transition matrix over time t. However, perhaps because of inadequate tools for matrix exponentiation in programming languages commonly used amongst statisticians or a belief that the necessary calculations are prohibitively expensive, statistical inference for continuous-time Markov chains with a large but finite state space is typically conducted via particle MCMC or other relatively complex inference schemes. When, as in many applications Q arises from a reaction network, it is usually sparse. We describe variations on known algorithms which allow fast, robust and accurate evaluation of the product of a non-negative vector with the exponential of a large, sparse rate matrix. Our implementation uses relatively recently developed, efficient, linear algebra tools that take advantage of such sparsity. We demonstrate the straightforward statistical application of the key algorithm on a model for the mixing of two alleles in a population and on the Susceptible-Infectious-Removed epidemic model.