Abstract
A genealogical tree based particle model for drawing approximate samples from the conditional path-distributions of a Markov chain with respect to its terminal values is presented. This path-particle evolution model can be interpreted as the historical process associated to a sequence of interacting Metropolis Markov chains. This novel class of interacting models can also be used to obtain approximate samples from a given target distribution which is only known up to a normalizing constant. We design an original Feynman–Kac modeling technique for studying the asymptotic analysis of these path-particle and Metropolis type simulation models. We provide precise convergence results as the time or the size of the systems tends to infinity. In contrast to the traditional Metropolis model we show that the decays to equilibrium do not depend on the nature of the desired limiting distribution.
Keywords: Interacting particle systems, genetic algorithms, genealogical trees, Feynman–Kac formulae, Metropolis algorithm, Markov chain Monte Carlo.
MSC (2000): 65C05, 65C35, 65C40
Keywords
- Markov Chain
- Particle Model
- Simulated Annealing Algorithm
- Gibbs Measure
- Target Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Del Moral, P., Doucet, A. (2003). On a Class of Genealogical and Interacting Metropolis Models. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-40004-2_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20520-3
Online ISBN: 978-3-540-40004-2
eBook Packages: Springer Book Archive
