Signal decompositions using trans-dimensional Bayesian methods.
type: Dataset
description: This thesis addresses the challenges encountered when dealing with signal decomposition problems with an unknown number of components in a Bayesian framework. Particularly, we focus on the issue of summarizing the variable-dimensional posterior distributions that typically arise in such problems. Such posterior distributions are defined over union of subspaces of differing dimensionality, and can be sampled from using modern Monte Carlo techniques, for instance the increasingly popular Reversible-Jump MCMC (RJ-MCMC) sampler. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. One of the main challenges that needs to be addressed to this end is the label-switching issue, which is caused by the invariance of the posterior distribution to the permutation of the components. We propose a novel approach to this problem, which consists in approximating the complex posterior of interest by a “simple”—but still variable-dimensional parametric distribution. We develop stochastic EM-type algorithms, driven by the RJ-MCMC sampler, to estimate the parameters of the model through the minimization of a divergence measure between the two distributions. Two signal decomposition problems are considered, to show the capability of the proposed approach both for relabeling and for summarizing variable dimensional posterior distributions: the classical problem of detecting and estimating sinusoids in white Gaussian noise on the one hand, and a particle counting problem motivated by the Pierre Auger project in astrophysics on the other hand.
landing page: https://theses.hal.science/tel-00765464
identifier: NNT: 2012SUPL0005
keyword: analyse-spectrale
keyword: bayesian-statistics
keyword: infoeu-reposemanticsdoctoralthesis
keyword: methodes-de-simulation-de-monte-carlo
keyword: monte-carlo-simulation-methods
keyword: signal-processing
keyword: spectral-analysis
keyword: spiotherengineering-sciences-physicsother
keyword: statistique-bayesienne
keyword: theses
keyword: traitement-du-signal
issued: 2026-05-30T23:20:40.283149
modified: 2026-05-30T23:20:40.283155
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Signal decompositions using trans-dimensional Bayesian methods.
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00765464
issued: 2026-05-30T23:20:40.424913
modified: 2026-05-30T23:20:40.222363