Hit-and-run, a class of MCMC samplers that converges to general multivariate distributions, is known to be unique in its ability to mix fast for uniform distributions over convex bodies. In particular, its rate of con...
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Hit-and-run, a class of MCMC samplers that converges to general multivariate distributions, is known to be unique in its ability to mix fast for uniform distributions over convex bodies. In particular, its rate of convergence to a uniform distribution is of a low order polynomial in the dimension. However, when the body of interest is difficult to sample from, typically a hyperrectangle is introduced that encloses the original body, and a one-dimensional acceptance/rejection is performed. The fast mixing analysis of hit-and-run does not account for this one-dimensional sampling that is often needed for implementation of the algorithm. Here we show that the effect of the size of the hyperrectangle on the efficiency of the algorithm is only a linear scaling effect. We also introduce a variation of hit-and-run that accelerates the sampler and demonstrate its capability through a computational study.
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