Jeff Rosenthal, University of Toronto, Canada

Title: Coupling and Ergodicity of Adaptive MCMC

Abstract:

Adaption is a very tempting method of automating and improving the tuning
of MCMC algorithms. However, natural-seeming adaptive schemes often fail
to preserve the stationary distribution, thus destroying the fundamental
ergodicity properties necessary for MCMC algorithms to be useful.
In this talk, we will first present some examples where adaption fails.
We will then present some simple conditions which ensure ergodicity and
stationarity of the specified target distribution. The proofs involve
intuitive bivariate coupling constructions.

This is joint work with Y. Atchade and with G.O. Roberts.

Note: One of the examples to be used in the talk is described in the
java applet here