Antithetic Coupling for Perfect Sampling

This paper reports some initial investigations of the use of antithetic variates in perfect sampling. A simple random walk example is presented to illustrate the key ingredients of antithetic coupling for perfect sampling as well as its potential benefit. A key step in implementing antithetic coupling is to generate random variates that are negatively associated, a stronger condition than negative correlation as it requires that the variates remain non-positively correlated after any (component-wise) monotone transformations have been applied. For , this step is typically trivial (e.g., by taking and , where ) and it constitutes much of the common use of antithetic variates in Monte Carlo simulation. Our emphasis is on because we have observed some general gains in going beyond the commonly used pair of antithetic variates. We discuss several ways of generating negatively associated random variates for arbitrary , and our comparison generally favors Iterative Latin Hypercube Sampling.