## Improving Markov Chain Monte Carlo Estimators by
Coupling to an Approximating Chain

**Ruxandra L. Pinto,
Dept. of Statistics, University of Toronto**

Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science, University of Toronto
We show how large improvements in the accuracy of MCMC estimates for
posterior expectations can sometimes be obtained by coupling a Markov
chain that samples from the posterior distribution with a chain that
samples from a Gaussian approximation to the posterior. Use of this
method requires a coupling scheme that produces high correlation
between the two chains. An efficient estimator can then be
constructed that exploits this correlation, provided an accurate value
for the expectation under the Gaussian approximation can be found,
which for simple functions can be done analytically. Good coupling
schemes are available for many Markov chain samplers, including Gibbs
sampling with standard conditional distributions. For many
moderate-dimensional problems, the improvement in accuracy using this
method will be much greater than the overhead from simulating a second
chain.

Technical Report No. 0101, Dept. of Statistics, University of Toronto
(February 2001), 13 pages:
postscript,
pdf.