Efficiency and time-dependent cross correlations in multivariable Monte Carlo updating.

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.