The Metropolis Hastings algorithm: introduction and optimal scaling of the transient phase | Vidéo | Carmin.tv

00:00:00 / 00:00:00

The Metropolis Hastings algorithm: introduction and optimal scaling of the transient phase

De Benjamin Jourdain

Apparaît dans les collections : CEMRACS - Summer school: Numerical methods for stochastic models: control, uncertainty quantification, mean-field / CEMRACS - École d'été : Méthodes numériques pour équations stochastiques : contrôle, incertitude, champ moyen, Ecoles de recherche

We first introduce the Metropolis-Hastings algorithm. We then consider the Random Walk Metropolis algorithm on $R^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one dimensional law. It is well-known that, in the limit $n$ tends to infinity, starting at equilibrium and for an appropriate scaling of the variance and of the timescale as a function of the dimension $n$, a diffusive limit is obtained for each component of the Markov chain. We generalize this result when the initial distribution is not the target probability measure. The obtained diffusive limit is the solution to a stochastic differential equation nonlinear in the sense of McKean. We prove convergence to equilibrium for this equation. We discuss practical counterparts in order to optimize the variance of the proposal distribution to accelerate convergence to equilibrium. Our analysis confirms the interest of the constant acceptance rate strategy (with acceptance rate between 1/4 and 1/3).

Informations sur la vidéo

Date de captation 19/07/2017
Date de publication 30/07/2017
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19199403
Citer cette vidéo Jourdain, Benjamin (19/07/2017). The Metropolis Hastings algorithm: introduction and optimal scaling of the transient phase. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19199403
URL https://dx.doi.org/10.24350/CIRM.V.19199403

Domaine(s)

Bibliographie

Jourdain, B., Lelièvre, T., & Miasojedow, B. (2015). Optimal scaling for the transient phase of the random walk Metropolis algorithm: the mean-field limit. The Annals of Applied Probability, 25(4), 2263-2300 - http://dx.doi.org/10.1214/14-AAP1048
Jourdain, B., Lelièvre, T., & Miasojedow, B. (2014). Optimal scaling for the transient phase of Metropolis Hastings algorithms: the longtime behavior. Bernoulli, 20(4), 1930-1978 - http://dx.doi.org/10.3150/13-BEJ546

Codes MSC

Document(s)

http://smai.emath.fr/cemracs/cemracs17/Slides/jourdain.pdf

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2024

Donner son avis