The Short-Cut Metropolis Method
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.