Abstract
Partial Rejection Sampling is an algorithmic approach to obtaining a perfect sample from a specified distribution. The objects to be sampled are assumed to be represented by a number of random variables. In contrast to classical rejection sampling, in which all variables are resampled until a feasible solution is found, partial rejection sampling aims at greater efficiency by resampling only a subset of variables that ‘go wrong’. Partial rejection sampling is closely related to Moser and Tardos’ algorithmic version of the Lovász Local Lemma, but with the additional requirement that a specified output distribution should be met. This article provides a largely self-contained account of the basic form of the algorithm and its analysis. Working within a unified framework allows a clean expression of the running time, and clarifies the scope for nondeterminism in its implementation.
Acknowledgments
The treatment of PRS presented here draws on many sources, in some cases heavily. Particularly influential are the works of Moser and Tardos [32], Knuth [27], Kolipaka and Szegedy [28] and Viennot [38]. I also learned a great deal through collaboration with Heng Guo. Finally, in retrospect, it is remarkable how many of the ideas behind PRS were already present in the work of Propp and Wilson [34] on cycle-popping.
I thank the referees for a thorough reading of the manuscript, encouraging remarks, and insightful comments.
Citation
Mark Jerrum. "Fundamentals of partial rejection sampling." Probab. Surveys 21 171 - 199, 2024. https://doi.org/10.1214/24-PS29
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