  A general methodology is presented for the construction and effective use of
control variates for reversible MCMC samplers. The values of the coefficients
of the optimal linear combination of the control variates are computed, and
adaptive, consistent MCMC estimators are derived for these optimal
coefficients. All methodological and asymptotic arguments are rigorously
justified. Numerous MCMC simulation examples from Bayesian inference
applications demonstrate that the resulting variance reduction can be quite
dramatic.
