Estimating parameters in stochastic compartmental models using Markov chain methods

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.