  Practitioners of Markov chain Monte Carlo (MCMC) may hesitate to use random
walk Metropolis-Hastings algorithms, especially variable-at-a-time algorithms
with many parameters, because these algorithms require users to select values
of tuning parameters (step sizes). These algorithms perform poorly if the step
sizes are set to be too low or too high. We show in this paper that it is not
difficult for an algorithm to tune these step sizes automatically to obtain a
desired acceptance probability, since the logit of the acceptance probability
is very nearly linear in the log of the step size, with known slope
coefficient. These ideas work in most applications, including single parameter
or block moves on the linear, log, or logit scales. We discuss the
implementation of this algorithm in the software package YADAS.
