Generating beta variates via patchwork rejection

Abstract

--ZusammenfassungGenerating Beta Variates via Patchwork Rejection. A new algorithm for sampling from beta(p,q) distributions with parameters p > 1, q > 1 is developed. It is based on a method by Minh [9] which improves acceptance-rejection sampling in the main part of the distributions. Additionally, transformed uniform deviates can often be accepted immediately, so that much fewer than two uniforms are needed for one beta variate, on the average. The remaining tests for acceptance are enhanced by 'squeezes'. Experiments covering a wide range of pairs (p, q) showed improvements in speed over competing algorithms in most cases.

Evaluation of Beta Generation Algorithms

“…On the other hand, algorithm B4PE outperforms all competing algorithms when is close to 1 and is large, while algorithm BPRS outperforms all competing algorithms for other cases. In general, the result is consistent with the work done by Zechner and Stadlober (1993). For the statistical software packages, we see that Matlab performs uniformly better than R and SAS in this case.…”

“…3.2) by comparing with the state-of-the-art algorithms introduced by Sakasegawa (1983) and Zechner and Stadlober (1993). We first consider the beta variates with < 1, wherein algorithms to be compared are Kennedy's MK, Jöhnk's method (JK), Sakasegawa's B00, Cheng's BC, and the Table 1, wherein Kennedy's MK algorithm was executed under three tolerance levels = 10 −2 , 10 −3 , and 10 −4 .…”

“…These algorithms all belong to the class of stratified rejection methods, in which piece-wise envlopes and exponentials are applied in the center and tails of the desired beta distribution, respectively. Zechner and Stadlober (1993) proposed two algorithms that are valid for > 1. These two algorithms are called BPRS and BPRB, which improve acceptance/rejection in the center of the desired beta distribution by using the idea of patchwork rejection.…”

Evaluation of algorithms for generating Dirichlet random vectors

“…• For α, β < 1, choose Kennedy's MK algorithm [20] if α + β > 1.2; otherwise, choose the B00 algorithm [21]; • For α < 1 < β or α > 1 > β, choose the B01 algorithm [21]; • For α, β > 1, choose the B4PE algorithm [22] if one parameter is close to 1 and the other is large (say > 4); otherwise, choose the BPRS algorithm [23].…”

Efficient sampling of random permutations

“…The hypergeometric distribution can be sampled quite efficiently, see [18,23,24]. Its computational cost is dominated by the calls to a random generator subroutine.…”