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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Gibson, G.J., Renshaw, E. Likelihood estimation for stochastic compartmental models using Markov chain methods. Statistics and Computing 11, 347–358 (2001). https://doi.org/10.1023/A:1011973120681
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DOI: https://doi.org/10.1023/A:1011973120681