Ph.D. Thesis: Particle Markov Chain Monte Carlo
Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC)
methods have emerged as the two main tools to sample from
high-dimensional probability distributions. Although asymptotic
convergence of MCMC algorithms is ensured under weak assumptions, the
performance of these latters is unreliable when the proposal
distributions used to explore the space are poorly chosen and/or if
highly correlated variables are updated independently. In this thesis
we propose a new Monte Carlo framework in which we build efficient
high-dimensional proposal distributions using SMC methods. This allows
us to design effective MCMC algorithms in complex scenarios where
standard strategies fail. We demonstrate these algorithms on a number
of example problems, including simulated tempering, non-linear
non-Gaussian state-space model, and protein folding.
Publications
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Ph.D. Thesis
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Christophe Andrieu, Arnaud Doucet, and Roman Holenstein.
"Particle Markov Chain Monte Carlo."
Journal of the Royal Statistical Society B (2009), to appear
Presented at the
Ordinary Meeting of the Royal Statistical Society
on Oct 14th, 2009.
(preprint)
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Christophe Andrieu, Arnaud Doucet, and Roman Holenstein.
"Particle Markov Chain Monte Carlo for efficient Numerical Simulation."
Lecture Notes in Statistics, Springer-Verlag, (2008), to appear.
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Christophe Andrieu, Arnaud Doucet, and Roman Holenstein,
"Particle
Markov Chain Monte Carlo,"
poster and oral presentation given at
the
Opening Workshop for the SAMSI program on Sequential Monte Carlo
Methods, Research Triangle Park,
North Carolina, USA (September 2008)
- Roman Holenstein and Arnaud Doucet, Particle Markov Chain Monte
Carlo, AdapMC: New Directions in Monte Carlo Methods, Fleurance,
France, June 2007. (pdf)
Collaborators
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