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An adaptive Monte-Carlo Markov chain algorithm for inference from mixture signals
Bardenet R., Kégl B.
Dans Journal of Physics: Conference Series - 14th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2011), Uxbridge : Royaume-Uni (2011) - http://hal.in2p3.fr/in2p3-00714497
Informatique/Algorithme et structure de données
An adaptive Monte-Carlo Markov chain algorithm for inference from mixture signals
R. Bardenet1, 2, 3, B. Kégl1, 2, 3
1 :  LAL - Laboratoire de l'Accélérateur Linéaire
http://www.lal.in2p3.fr/
CNRS : UMR8607 – IN2P3 – Université Paris XI - Paris Sud
Centre Scientifique d'Orsay B.P. 34 91898 ORSAY Cedex
France
2 :  LRI - Laboratoire de Recherche en Informatique
http://www.lri.fr/
CNRS : UMR8623 – Université Paris Sud
LRI - Bâtiments 650-660 Université Paris-Sud 91405 Orsay Cedex
France
3 :  INRIA Saclay - Ile de France - TAO
http://tao.lri.fr/tiki-index.php
INRIA – CNRS : UMR8623 – Université Paris XI - Paris Sud
France
Pierre Auger
Adaptive Metropolis (AM) is a powerful recent algorithmic tool in numerical Bayesian data analysis. AM builds on a well-known Markov Chain Monte Carlo algorithm but optimizes the rate of convergence to the target distribution by automatically tuning the design parameters of the algorithm on the fly. Label switching is a major problem in inference on mixture models because of the invariance to symmetries. The simplest (non-adaptive) solution is to modify the prior in order to make it select a single permutation of the variables, introducing an identifiability constraint. This solution is known to cause artificial biases by not respecting the topology of the posterior. In this paper we describe an online relabeling procedure which can be incorporated into the AM algorithm. We give elements of convergence of the algorithm and identify the link between its modified target measure and the original posterior distribution of interest. We illustrate the algorithm on a synthetic mixture model inspired by the muonic water Cherenkov signal of the surface detectors in the Pierre Auger Experiment.

Communications avec actes
2012
09/2011
Journal of Physics: Conference Series
internationale
368
Liliana Teodorescu, David Britton, Nigel Glover, Gudrun Heinrich, Jérôme Lauret, Axel Naumann, Thomas Speer, Pedro Teixeira-Dias
012044
IOP Publishing

14th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2011)
Uxbridge
Royaume-Uni
05/09/2011
09/09/2011
Rémi Bardenet

LAL 12-250