Empirical supremum rejection sampling

Brian S. Caffo, James G. Booth, A. C. Davison

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)745-754
Number of pages10
Issue number4
StatePublished - 2002


  • Accept-reject
  • Candidate distribution
  • Monte Carlo
  • Sample maximum
  • Super-efficient estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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