The application of continuous‐time Markov chain models in the analysis of choice flume experiments

2021 ◽  
Author(s):  
Michael A. Spence ◽  
Evalyne W. Muiruri ◽  
David L. Maxwell ◽  
Scott Davis ◽  
Dave Sheahan
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Continuous Time Markov Chain ◽  
Flume Experiments ◽  
Markov Chain Models

Continuous Time Markov Chain Models of Voltage Gating of Gap Junction Channels

2014 ◽  
Vol 43 (2) ◽  
Author(s):  
H. Pranevicius ◽  
M. Pranevicius ◽  
O. Pranevicius ◽  
M. Snipas ◽  
N. Paulauskas ◽  
...  
Keyword(s):  
Markov Chain ◽  
Gap Junction ◽  
Continuous Time ◽  
Voltage Gating ◽  
Continuous Time Markov Chain ◽  
Gap Junction Channels ◽  
Markov Chain Models

scholarly journals Estimating animal utilization densities using continuous‐time Markov chain models

2018 ◽  
Vol 9 (5) ◽  
pp. 1232-1240 ◽  
Author(s):  
Kenady Wilson ◽  
Ephraim Hanks ◽  
Devin Johnson
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Continuous Time Markov Chain ◽  
Markov Chain Models ◽  
Animal Utilization

Exact Inference for Continuous Time Markov Chain Models

1986 ◽  
Vol 53 (4) ◽  
pp. 653 ◽  
Author(s):  
John Geweke ◽  
Robert C. Marshall ◽  
Gary A. Zarkin
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Continuous Time Markov Chain ◽  
Exact Inference ◽  
Markov Chain Models

scholarly journals Continuous time Markov chain approaches for analyzing transtheoretical models of health behavioral change: A case study and comparison of model estimations

2016 ◽  
Vol 27 (2) ◽  
pp. 593-607 ◽  
Author(s):  
Junsheng Ma ◽  
Wenyaw Chan ◽  
Barbara C Tilley
Keyword(s):  
Markov Chain ◽  
Maximum Likelihood ◽  
Bayesian Approach ◽  
Transtheoretical Model ◽  
Continuous Time ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Standard Errors ◽  
Continuous Time Markov Chain ◽  
Markov Chain Models

Continuous time Markov chain models are frequently employed in medical research to study the disease progression but are rarely applied to the transtheoretical model, a psychosocial model widely used in the studies of health-related outcomes. The transtheoretical model often includes more than three states and conceptually allows for all possible instantaneous transitions (referred to as general continuous time Markov chain). This complicates the likelihood function because it involves calculating a matrix exponential that may not be simplified for general continuous time Markov chain models. We undertook a Bayesian approach wherein we numerically evaluated the likelihood using ordinary differential equation solvers available from the gnu scientific library. We compared our Bayesian approach with the maximum likelihood method implemented with the R package MSM. Our simulation study showed that the Bayesian approach provided more accurate point and interval estimates than the maximum likelihood method, especially in complex continuous time Markov chain models with five states. When applied to data from a four-state transtheoretical model collected from a nutrition intervention study in the next step trial, we observed results consistent with the results of the simulation study. Specifically, the two approaches provided comparable point estimates and standard errors for most parameters, but the maximum likelihood offered substantially smaller standard errors for some parameters. Comparable estimates of the standard errors are obtainable from package MSM, which works only when the model estimation algorithm converges.

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