Optimal Scaling of the Random Walk Metropolis algorithm - with Gareth Roberts.

We derived simple exact formulae for expected square jump distance (a measure of efficiency) and expected acceptance rate for a RWM on any elliptically symmetric unimodal target using any proposal. These formulae are true for real, finite dimensional targets.

We then examined behaviour in the limit as dimension tends to infinity, obtaining the asymptotically optimal acceptance rate of 0.234 as a special case of a more general set of results.

Poster given at Valencia 2006.

A paper is currently in preparation.