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SUMMARY:Gaussian Approximation and Output Analysis for High-Dimensional MC
 MC - Ardjen Pengel (University of Cambridge)
DTSTART:20241126T142000Z
DTEND:20241126T151000Z
UID:TALK221530@talks.cam.ac.uk
DESCRIPTION:The widespread use of Markov Chain Monte Carlo (MCMC) methods 
 for high-dimensional applications has motivated research into the scalabil
 ity of these algorithms with respect to the dimension of the problem. Desp
 ite this\, numerous problems concerning output analysis in high-dimensiona
 l settings have remained unaddressed. We present novel quantitative Gaussi
 an approximations for a broad range of both continuous and discrete time M
 CMC algorithms. Notably\, we analyse the dependency of the obtained approx
 imation errors on the dimension of both the target distribution and the fe
 ature space. We demonstrate how these Gaussian approximations can be appli
 ed in output analysis. This includes central limit theorems and variance e
 stimation in the high-dimensional setting. We give quantitative convergenc
 e bounds for termination criteria and show that the termination time of a 
 wide class of MCMC algorithms scales polynomially in dimension while ensur
 ing a desired level of precision. Our results offer guidance to practition
 ers for obtaining appropriate standard errors and deciding the minimum sim
 ulation effort of MCMC algorithms in both multivariate and high-dimensiona
 l settings.\nCo-authors: Jun Yang (University of Copenhagen) and Zhou Zhou
 (University of Toronto)
LOCATION:Seminar Room 1\, Newton Institute
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