Thesis of Martin Rouault

Monte Carlo,Integration,Gibbs distributions,

Markov chain Monte Carlo algorithms (MCMC) are numerical integration algorithms that are ubiquitous in high-dimensional statistical inference and Bayesian machine learn- ing. The crux is to sample a carefully-chosen Markov chain in the domain of integration, and average the evaluations of the integrand along that chain. However, MCMC is slow: the resulting estimators have a mean squared error that decreases as 1/N , where N is the number of time steps in the Markov chain sample. . Following the intuition that repulsiveness brings qualitative variance reduction, we propose to leverage repulsive stochastic processes, to build parallel MCMC algorithms that quickly and jointly explore the domain of integration.

Jury

M. Rémi BARDENET Directeur de recherche CNRS, CRIStAL, Université de Lille Directeur de thèse, M. Nicolas CHOPIN Professeur ENSAE, Institut Polytechnique de Paris Rapporteur, M. Djalil CHAFAÏ Professeur des universités Ceremade Université Paris-Dauphine - PSL, DMA Ecole Normale Supérieure (Paris) - PSL Rapporteur, Mme Mylène MAÏDA Professeure des universités Laboratoire Paul Painlevé, Université de Lille Co-directrice de thèse, Mme Alice GUIONNET Directrice de recherche UMPA, Ecole Normale Supérieure de Lyon Examinatrice, M. Carlos BELTRÁN Professor Universidad de Cantabria Examinateur, Mme Anna KORBA Assistant professor ENSAE, Institut Polytechnique de Paris Examinatrice.

Thesis of the team SIGMA defended on 19/03/2026