Likelihood estimation for stochastic compartmental models using Markov chain methods |
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Authors: | Gavin J. Gibson Eric Renshaw |
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Affiliation: | (1) Biomathematics and Statistics Scotland, James Clerk Maxwell Building, The King's Buildings, Edinburgh, EH9 3JZ, UK;(2) Department of Statistics and Modelling Science, University of Strathclyde, Glasgow, G1 1XH, UK |
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Abstract: | This paper presents a method for estimating likelihood ratios for stochastic compartment models when only times of removals from a population are observed. The technique operates by embedding the models in a composite model parameterised by an integer k which identifies a switching time when dynamics change from one model to the other. Likelihood ratios can then be estimated from the posterior density of k using Markov chain methods. The techniques are illustrated by a simulation study involving an immigration-death model and validated using analytic results derived for this case. They are also applied to compare the fit of stochastic epidemic models to historical data on a smallpox epidemic. In addition to estimating likelihood ratios, the method can be used for direct estimation of likelihoods by selecting one of the models in the comparison to have a known likelihood for the observations. Some general properties of the likelihoods typically arising in this scenario, and their implications for inference, are illustrated and discussed. |
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