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Multiple projection MCMC algorithms on submanifolds

Tony Lelièvre 1, 2 Gabriel Stoltz 1, 2 Wei Zhang 3
2 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02515267
Contributor : Tony Lelièvre Connect in order to contact the contributor
Submitted on : Monday, March 23, 2020 - 2:17:14 PM
Last modification on : Thursday, February 4, 2021 - 4:50:01 PM

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  • HAL Id : hal-02515267, version 1
  • ARXIV : 2003.09402

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Tony Lelièvre, Gabriel Stoltz, Wei Zhang. Multiple projection MCMC algorithms on submanifolds. 2020. ⟨hal-02515267⟩

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