The acceptance-complement method revisited

2026-07-23

AI Summary

Traditional rejection sampling methods suffer from unstable efficiency due to their geometrically distributed runtimes. This work proposes a general accept-complement approach that leverages the properties of log-concave densities and knowledge of their mode locations to generate random variates with deterministic constant-time complexity. The method applies universally to any log-concave distribution accessible via black-box evaluation, encompassing important families such as Gamma and Beta distributions. By enabling efficient “one-liner” sampling, it establishes a unified and practical framework for random number generation that overcomes the variability inherent in classical rejection sampling while maintaining broad applicability.

Abstract

We revisit the acceptance-complement method in random variate generation and show how it can replace the rejection method in many examples. While the rejection method has geometrically distributed execution times, the acceptance-complement method has a constant (deterministic) run time and qualifies as a ``one-liner''. We show how this method can be used to efficiently generate random variates from several distributions, such as the gamma and beta. In addition, we show that there is an acceptance-complement method that is valid for all log-concave densities with known location of the mode and black-box type access to the density.

Problem

• random variate generation
• rejection method
• acceptance-complement method
• log-concave densities
• constant run time

Innovation

• acceptance-complement method
• random variate generation
• log-concave densities
• constant-time sampling
• rejection sampling alternative