A joint likelihood approach to the analysis of length of stay data utilising the continuous-time hidden Markov model and Coxian phase-type distribution

AbstractMotivationAccumulating evidence has highlighted the importance of microbial interaction networks. Methods have been developed for estimating microbial interaction networks, of which the generalized Lotka-Volterra equation (gLVE)-based method can estimate a directed interaction network. The previous gLVE-based method for estimating microbial interaction networks did not consider time-varying interactions.ResultsIn this study, we developed unsupervised learning based microbial interaction inference method using Bayesian estimation (Umibato), a method for estimating time-varying microbial interactions. The Umibato algorithm comprises Gaussian process regression (GPR) and a new Bayesian probabilistic model, the continuous-time regression hidden Markov model (CTRHMM). Growth rates are estimated by GPR, and interaction networks are estimated by CTRHMM. CTRHMM can estimate time-varying interaction networks using interaction states, which are defined as hidden variables. Umibato outperformed the existing methods on synthetic datasets. In addition, it yielded reasonable estimations in experiments on a mouse gut microbiota dataset, thus providing novel insights into the relationship between consumed diets and the gut microbiota.AvailabilityThe C++ and python source codes of the Umibato software are available at http://github.com/shion-h/[email protected], [email protected]

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Hidden-Markov-Model-Based Asynchronous Filter Design of Nonlinear Markov Jump Systems in Continuous-Time Domain

IEEE Transactions on Cybernetics ◽

10.1109/tcyb.2018.2824799 ◽

2019 ◽

Vol 49 (6) ◽

pp. 2294-2304 ◽

Cited By ~ 23

Author(s):

Shanling Dong ◽

Zheng-Guang Wu ◽

Ya-Jun Pan ◽

Hongye Su ◽

Yang Liu

Keyword(s):

Markov Model ◽

Hidden Markov Model ◽

Time Domain ◽

Continuous Time ◽

Filter Design ◽

Hidden Markov ◽

Markov Jump ◽

Markov Jump Systems ◽

Model Based ◽

Jump Systems

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Time discretization of continuous-time filters for hidden Markov model parameter estimation

[1992] Proceedings of the 31st IEEE Conference on Decision and Control ◽

10.1109/cdc.1992.371026 ◽

2005 ◽

Cited By ~ 1

Author(s):

M.R. James ◽

V. Krishnamurthy ◽

F. Le Gland

Keyword(s):

Parameter Estimation ◽

Markov Model ◽

Hidden Markov Model ◽

Continuous Time ◽

Hidden Markov ◽

Time Discretization ◽

Model Parameter ◽

Model Parameter Estimation ◽

Continuous Time Filters

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A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores

10.1101/223875 ◽

2017 ◽

Cited By ~ 2

Author(s):

Lekha Patel ◽

Nils Gustafsson ◽

Yu Lin ◽

Raimund Ober ◽

Ricardo Henriques ◽

...

Keyword(s):

Markov Model ◽

Hidden Markov Model ◽

Continuous Time ◽

Hidden Markov ◽

Super Resolution ◽

Information Criterion ◽

Switching Behavior ◽

Time Signal ◽

Full Characterization ◽

Continuous Time Process

AbstractFluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.

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