Tamás Papp

Dimensional scaling of coupled MCMC algorithms

Couplings can be used to remove the bias of MCMC estimators — however, it's not clear how one can design couplings which scale well to high dimensions. I'll address this question for the Random Walk Metropolis, connecting coupled MCMC sampling with the optimal scaling literature.

In particular, I'll introduce a coupling which is optimal in an asymptotic sense and overcomes the shortcomings of previous proposals. Our main technical tools will be high-dimensional ODE limits for Gaussian targets.

This talk is based on joint work with Chris Sherlock (arxiv:2211.12585).