UCPH Statistics Seminar: Ardjen Pengel

Title: Gaussian approximation and variance estimation for high-dimensional MCMC

Speaker: Ardjen Pengel from TU Delft

Abstract: We consider the problem of sampling from high-dimensional probability distributions, a task encountered in numerous settings such as machine learning and Bayesian inference for high-dimensional statistical models. We present Gaussian approximation results for a broad range of Markov Chain Monte Carlo (MCMC) algorithms. These results characterise the error involved in approximating the partial sums of an MCMC algorithm using a Gaussian process with the same mean and covariance structure. Notably, we analyse the dependency of the obtained bounds on the dimension of the target distribution. Furthermore, we show how these Gaussian approximation results can be used to analyse estimators of the asymptotic variance in settings with a dependence structure. By providing dimension-dependent bounds, we can appropriately choose the tuning parameters for variance estimation methods in high-dimensional settings. An important application is the estimation of the MCMC standard error, which is required for assessing the uncertainty quantification of the sampling algorithm and computing many convergence diagnostics.