Marco Läubli: Particle Markov Chain Monte Carlo for Partially Observed Markov Jump Processes

Adviser: Prof. Dr. Hans-Rudolf Künsch

August 2011

Abstract:

The goal of the thesis was to investigate, understand and implement the so called particle Markov chain Monte Carlo (PMCMC) algorithms introduced by Andrieu, Doucet, and Holenstein (2010) and to compare them to classical MCMC algorithms. The PMCMC algorithms are introduced in the framework of state space models. Their key idea is to use sequential Monte Carlo (SMC) algorithms to construct efficient highdimensional proposals for MCMC algorithms. The performance of the algorithms is examined on a simple birth-death process in discrete time as well as on the stochastic Oregonator, an idealized model of the Belousov-Zhabotinskii non-linear chemical oscillator. In summary it can be said that the PMCMC algorithms produce satisfactory results even when using only standard components and they require comparably little problem-specific design effort from the user's side. On the other hand it must be mentioned that the computational effort, compared to classical methods, is tremendous and a serious drawback.

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