I show how one can modify the random-walk Metropolis MCMC method in such a way that a sequence of modified Metropolis updates takes little computation time when the rejection rate is outside a desired interval. This allows one to effectively adapt the scale of the Metropolis proposal distribution, by performing several such ``short-cut'' Metropolis sequences with varying proposal stepsizes. Unlike other adaptive Metropolis schemes, this method converges to the correct distribution in the same fashion as the standard Metropolis method.
Technical Report No. 0506, Dept. of Statistics, University of Toronto (August 2005), 28 pages: postscript, pdf.
Also available from arXiv.org.
You can also get the program used for the tests in this paper.