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2017 Geometric ergodicity of Rao and Teh’s algorithm for Markov jump processes and CTBNs
Błażej Miasojedow, Wojciech Niemiro
Electron. J. Statist. 11(2): 4629-4648 (2017). DOI: 10.1214/17-EJS1348


Rao and Teh (2012, 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. A similar result is also proved for a special version of the algorithm, used for probabilistic inference in Continuous Time Bayesian Networks.


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Błażej Miasojedow. Wojciech Niemiro. "Geometric ergodicity of Rao and Teh’s algorithm for Markov jump processes and CTBNs." Electron. J. Statist. 11 (2) 4629 - 4648, 2017.


Received: 1 November 2016; Published: 2017
First available in Project Euclid: 18 November 2017

zbMATH: 06816627
MathSciNet: MR3724970
Digital Object Identifier: 10.1214/17-EJS1348

Primary: 65C40
Secondary: 60J27 , 65C05

Keywords: continuous time Bayesian network , Continuous time Markov processes , drift condition , geometric ergodicity , Hidden Markov models , MCMC , posterior sampling , small set


Vol.11 • No. 2 • 2017
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