An exact Gibbs sampler for the Markov‐modulated Poisson process

Paul Fearnhead and Chris Sherlock

Journal of the Royal Statistical Society Series B, 2006, vol. 68, issue 5, 767-784

Abstract: Summary. A Markov‐modulated Poisson process is a Poisson process whose intensity varies according to a Markov process. We present a novel technique for simulating from the exact distribution of a continuous time Markov chain over an interval given the start and end states and the infinitesimal generator, and we use this to create a Gibbs sampler which samples from the exact distribution of the hidden Markov chain in a Markov‐modulated Poisson process. We apply the Gibbs sampler to modelling the occurrence of a rare DNA motif (the Chi site) and to inferring regions of the genome with evidence of high or low intensities for occurrences of this site.

Date: 2006
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