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An exact Gibbs sampler for the Markov-modulated Poisson process

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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.
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Keywords: Forward–backward algorithm; Genome segmentation; Gibbs sampler

Document Type: Research Article

Affiliations: Lancaster University, UK

Publication date: November 1, 2006

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