Optimization of the antithetic Gibbs sampler for Gaussian Markov random fields

The efficiency of Markov chain Monte Carlo estimation suffers from the autocorrelation of successive iterations, which is typical for this sampling method. In order to improve the efficiency, antithetic methods attempt to reduce this autocorrelation or even introduce negative autocorrelation. In this paper the antithetic method is adopted to Gibbs sampling of the spatial correlation structure of Gaussian Markov random fields and a rule for the optimal choice of the antithetic parameter is developed. The antithetic Gibbs sampler turns out to perform much better than the classical Gibbs sampler and could compete with i.i.d. sampling, which indeed is usually intractable for this kind of application.