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Geometric ergodicity of Rao and Teh’s algorithm for homogeneous Markov jump processes

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  • Miasojedow, Błażej
  • Niemiro, Wojciech

Abstract

Rao and Teh (2013) introduced an efficient MCMC algorithm for sampling from the posterior distribution of a hidden Markov jump process. The algorithm is based on the idea of sampling virtual jumps. In the present paper we show that the Markov chain generated by Rao and Teh’s algorithm is geometrically ergodic. To this end we establish a geometric drift condition towards a small set. We work under the assumption that the parameters of the hidden process are known and the goal is to restore its trajectory.

Suggested Citation

  • Miasojedow, Błażej & Niemiro, Wojciech, 2016. "Geometric ergodicity of Rao and Teh’s algorithm for homogeneous Markov jump processes," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 1-6.
    • Handle: RePEc:eee:stapro:v:113:y:2016:i:c:p:1-6
    DOI: 10.1016/j.spl.2016.02.002
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    References listed on IDEAS

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    1. Paul Fearnhead & Chris Sherlock, 2006. "An exact Gibbs sampler for the Markov‐modulated Poisson process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 767-784, November.
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