A na¨ive way to implement the antithetic variable scheme is to use both U and (1-U) in an inversion simulation. Examine empirically whether this method leads to variance reduction for the distributions
To calculate the weights for the Rao-Blackwellized estimator of Section 4.6, it is necessary to derive properties of the distribution of the random variables in the Accept- Reject algorithm. The following problem is a rather straightforward exercise in distribution theory and is only made complicated by the stopping rule of the Accept-Reject algorithm.
