Identifying Markov Chain Models from Time-to-Event Data: An Algebraic Approach

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Dades bibliogràfiques
Publicat a:	Bulletin of Mathematical Biology vol. 87, no. 1 (Jan 2025), p. 11
Autor principal:	Radulescu, Ovidiu
Altres autors:	Grigoriev, Dima, Seiss, Matthias, Douaihy, Maria, Lagha, Mounia, Bertrand, Edouard
Publicat:	Springer Nature B.V.
Matèries:	Computer algebra Parameter identification Gene expression Markov chains Inverse problems Gene regulation Cell culture Laplace transforms Decomposition Survival analysis Markov analysis Recursive methods
Accés en línia:	Citation/Abstract Full Text Full Text - PDF
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Descripció
Resum:	Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we identify the transition rate parameters of the underlying Markov chain? For a specific class of solvable Markov models, we show this problem has a unique solution up to finite symmetry transformations, and we outline a recursive method for computing symbolic solutions for these models across any number of states. Using the Thomas decomposition technique from computer algebra, we further provide symbolic solutions for any model. Interestingly, different models with the same state count but distinct transition graphs can yield identical phase-type distributions. To distinguish among these, we propose additional properties beyond just the time to the next event. We demonstrate the method’s applicability by inferring transcriptional regulation models from single-cell transcription imaging data.
ISSN:	0092-8240 1522-9602 0007-4985
DOI:	10.1007/s11538-024-01385-y
Font:	Science Database