Perfect slice samplers (Q2767533)

The authors combine two powerful methods that have recently appeared in the Markov chain Monte Carlo literature, i.e. the slice sampler and perfect simulations. Section~2 contains a brief description of the simple slice sampler, together with a discussion of its properties. Analogously, Section~3 surveys perfect simulation based on stochastic recursive sequence. Section~4 is concerned with an explicit stochastic recursive sequence for the simple slice sampler, which can easily be used for perfect simple slice sampling when there is a maximal and minimal state with respect to the density ordering. By exploiting monotonicity properties of the slice sampler it is shown that a perfect version of the algorithm can be easily implemented, at least when the target distribution is bounded. Extensions to the cases where there is no maximal or minimal state are discussed in Section~5. Various, mainly spatial, examples and further extensions using more than one auxiliary variable are studied in Section~6. Finally, Section~7 contains some concluding remarks.