Martin Chak, Nikolas Kantas, Tony Lelièvre, Grigorios Pavliotis
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引用次数: 5
Abstract
We propose a procedure for optimising the friction matrix of underdamped Langevin dynamics when used for continuous time Markov Chain Monte Carlo. Starting from a central limit theorem for the ergodic average, we present a new expression of the gradient of the asymptotic variance with respect to friction matrix. In addition, we present an approximation method that uses simulations of the associated first variation/tangent process. Our algorithm is applied to a variety of numerical examples such as toy problems with tractable asymptotic variance, diffusion bridge sampling and Bayesian inference problem for high dimensional logistic regression.
期刊介绍：
The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains.
Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics.
Long papers are very welcome.
Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.
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