Efficient sampling from the PKBD distribution

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY
Lukas Sablica, Kurt Hornik, Josef Leydold
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引用次数: 0

Abstract

In this paper we present and analyze random number generators for the Poisson Kernel-Based Distribution (PKBD) on the sphere. We show that the only currently available sampling scheme presented in Golzy and Markatou (2020) can be improved by a better selection of hyper-parameters but still yields an unbounded rejection constant as the concentration parameter approaches 1. Furthermore, we introduce two additional and superior sampling methods for which boundedness in the above mentioned case can be obtained. The first method proposes initial draws from angular central Gaussian distribution and offers uniformly bounded rejection constants for a significant part of the PKBD parameter space. The second method uses adaptive rejection sampling and the results of Ulrich (1984) to sample from the projected Saw distribution (Saw, 1978). Finally, both new methods are compared in a simulation study.
从PKBD分布中有效采样
本文给出并分析了球上基于泊松核分布(PKBD)的随机数生成器。我们表明,Golzy和Markatou(2020)提出的目前唯一可用的采样方案可以通过更好地选择超参数来改进,但当浓度参数接近1时,仍然产生无界抑制常数。此外,我们还引入了另外两种更好的抽样方法,它们可以得到上述情况下的有界性。第一种方法从角中心高斯分布中提出初始提取,并为PKBD参数空间的重要部分提供均匀有界抑制常数。第二种方法使用自适应抑制采样和Ulrich(1984)的结果从预测的Saw分布(Saw, 1978)中采样。最后,在仿真研究中对两种方法进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
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