title: Efficiency and time-dependent cross correlations in multivariable Monte Carlo updating.
abstract: We show that any Monte Carlo (MC) algorithm using joint updates of more than a single variable at each step produces time-shifted correlations between variables-even if the equilibrium probabilities of the variables are independent. These spurious time-shifted correlations will affect both the magnitudes of correlation times and the values of optimal acceptance ratios. In particular, correlation times computed with local variables will not generally give the same predictions of efficiency or optimal acceptance ratios as those computed with global variables. Gelman, Roberts, and Gilks [Bayesian Statistics, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. R. M. Smith, Vol. 5 (Oxford University Press, 1996), pp. 599-607] have used a local measure of efficiency to prove a theorem for global MC updating that predicts an optimal acceptance ratio of 0.234 as the number of variables goes to infinity. We show that global measures of efficiency can produce different, and arguably more appropriate, optimal acceptance ratios. More importantly, global updating is inherently far less efficient than updating variables separately or in small groups. We suggest that previously determined optimal acceptance ratios and their implications for practical applications should be reconsidered in the context of these findings.
authors: Department of Mathematical Sciences, Carnegie-Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA.
authors: Christopher C J
authors: CC
authors: Potter
authors: Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA.
authors: Robert H
authors: RH
authors: Swendsen