Nüsken, N. and Reich, S.
(2019)
*Note on Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman
Sampler by Garbuno-Inigo, Hoffmann, Li and Stuart.*
arXive
.
pp. 1-6.
(Submitted)

Full text not available from this repository.

Official URL: https://arxiv.org/pdf/1908.10890.pdf

## Abstract

An interacting system of Langevin dynamics driven particles has been proposed forsampling from a given posterior density by Garbuno-Inigo, Hoffmann, Li and StuartinInteracting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler(arXiv:1903:08866v2). The proposed formulation is primarily studiedfrom a formalmean-field limit perspective, while the theoretical behaviour under afinite particlesize is left as an open problem. In this note we demonstrate that theparticle-basedcovariance interaction term requires a non-trivial correction. Wealso show that thecorrected dynamics samples exactly from the desired posterior provided that the em-pirical covariance matrix of the particle system remains non-singular and the posteriorlog-density satisfies the standard Bakry– ́Emery criterion.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2479 |

Deposited By: | Monika Drueck |

Deposited On: | 25 Nov 2020 12:44 |

Last Modified: | 25 Nov 2020 12:44 |

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