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Biometrika 2002 89(4):745-754; doi:10.1093/biomet/89.4.745
© 2002 by Biometrika Trust
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Empirical supremum rejection sampling

Brian S.Caffo1, James G.Booth2 and A.C. Davison3

1 Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205, U.S.Abcaffo{at}jhsph.edu 2 Department of Statistics, University of Florida, Gainesville, Florida 32611, U.S.A.jbooth{at}stat.ufl.edu 3 Institute of Mathematics, Swiss Federal Institute of Technology, 1015 Lausanne, Switzerland anthony.davison{at}epfl.ch

Rejection sampling thins out samples from a candidate density from which it is easy to simulate, to obtain samples from a more awkward target density.A prerequisite is knowledge of the finite supremum of the ratio of the target and candidate densities. This severely restricts application of the method because it can be difficult to calculate the supremum. We use theoretical argument and numerical work to show that a practically perfect sample may be obtained by replacing the exact supremum with the maximum obtained from simulated candidates. We also provide diagnostics for failure of the method caused by a bad choice of candidate distribution. The implication is that essentially no theoretical work is required to apply rejection sampling in many practical cases.

Key Words: Accept-reject; Candidate distribution; Monte Carlo; Sample maximum; Super-effcient estimator

Received April 2001. Revised January 2002


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