A Dirichlet Form approach to MCMC Optimal Scaling

Probability Seminar

Wilfrid Kendall (U of Warwick)

Thursday, April 27, 2017 -
4:15pm to 5:15pm
UNC, 125 Hanes Hall

In this talk I will discuss the use of Dirichlet forms to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis-Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form method has the added advantage of providing an explicit construction of the underlying infinite-dimensional context. In particular, this enables us directly to establish weak convergence to the relevant infinite-dimensional diffusion. Zanella, G., Kendall, W. S., & Bédard, M. (2016). A Dirichlet Form approach to MCMC Optimal Scaling. arXiv, 1606.01528, 22pp. URL: arxiv.org/abs/1606.01528 .