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Mathematical Medicine and Biology 1998 15(1):19-40; doi:10.1093/imammb/15.1.19
© 1998 by Institute of Mathematics and its Applications
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Estimating parameters in stochastic compartmental models using Markov chain methods

GAVIN J. GIBSON and ERIC RENSHAW

Biomathematics and Statistics Scotland, King's Buildings Mayfield Road, Edinburgh EH9 3JZ, UK
Department of Statistics and Modelling Science, Livingstone Tower, University of Strathclyde 26 Richmond Street, Glasgow G1 1XH, UK

Markov chain Monte Carlo methodology is presented for estimating parameters in stochastic compartmental models from incomplete observations of the corresponding Markov process. The methods, which are based on the Metropolis-Hastings algorithm, are developed in the context of epidemic models. Their use is illustrated for the particular case where only susceptible, infective, and removed states are represented using simulated realizations of the process. By comparing estimated likelihoods with theoretical forms, in cases where these can be derived, or with the known model parameters, we show that the methods can be used to provide meaningful estimates of parameters and parameter uncertainty. Potential applications of the techniques are also discussed.

Keywords: stochastic compartment models; parameter estimation; Markov chain Monte Carlo methods; hidden Markov models.


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Statistical Modeling, April 1, 2004; 4(1): 63 - 75.
[Abstract] [PDF]


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