A1123
Title: Output analysis for high-dimensional MCMC
Authors: Ardjen Pengel - University of Cambridge (United Kingdom) [presenting]
Abstract: The widespread use of Markov chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems concerning output analysis in high-dimensional settings have remained unaddressed. Novel quantitative Gaussian approximation results are presented for a broad range of MCMC algorithms. Notably, the dependency of the obtained approximation errors is analysed on the dimension of both the target distribution and the feature space. It is demonstrated how these Gaussian approximations can be applied in output analysis. This includes determining the simulation effort required to guarantee Markov chain central limit theorems and consistent estimation of both the variance and the effective sample size in high-dimensional settings. Quantitative convergence bounds are given for termination criteria, and it is shown that the termination time of a wide class of MCMC algorithms scales polynomially in dimension while ensuring a desired level of precision. The results offer guidance to practitioners for obtaining appropriate standard errors and deciding the minimum simulation effort of MCMC algorithms in both multivariate and high-dimensional settings.
