{"title":"Novel sampling method for the von Mises–Fisher distribution","authors":"","doi":"10.1007/s11222-024-10419-3","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>The von Mises–Fisher distribution is a widely used probability model in directional statistics. An algorithm for generating pseudo-random vectors from this distribution was suggested by Wood (Commun Stat Simul Comput 23(1):157–164, 1994), which is based on a rejection sampling scheme. This paper proposes an alternative to this rejection sampling approach for drawing pseudo-random vectors from arbitrary von Mises–Fisher distributions. A useful mixture representation is derived, which is a mixture of beta distributions with mixing weights that follow a confluent hypergeometric distribution. A condensed table-lookup method is adopted for sampling from the confluent hypergeometric distribution. A theoretical analysis investigates the amount of computation required to construct the condensed lookup table. Through numerical experiments, we demonstrate that the proposed algorithm outperforms the rejection-based method when generating a large number of pseudo-random vectors from the same distribution.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11222-024-10419-3","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
The von Mises–Fisher distribution is a widely used probability model in directional statistics. An algorithm for generating pseudo-random vectors from this distribution was suggested by Wood (Commun Stat Simul Comput 23(1):157–164, 1994), which is based on a rejection sampling scheme. This paper proposes an alternative to this rejection sampling approach for drawing pseudo-random vectors from arbitrary von Mises–Fisher distributions. A useful mixture representation is derived, which is a mixture of beta distributions with mixing weights that follow a confluent hypergeometric distribution. A condensed table-lookup method is adopted for sampling from the confluent hypergeometric distribution. A theoretical analysis investigates the amount of computation required to construct the condensed lookup table. Through numerical experiments, we demonstrate that the proposed algorithm outperforms the rejection-based method when generating a large number of pseudo-random vectors from the same distribution.
摘要 von Mises-Fisher 分布是定向统计中广泛使用的概率模型。伍德（Commun Stat Simul Comput 23(1):157-164, 1994）提出了一种从该分布生成伪随机向量的算法，该算法基于拒绝抽样方案。本文提出了从任意 von Mises-Fisher 分布中抽取伪随机向量的拒绝抽样方法的替代方案。本文导出了一种有用的混合表示法，即混合权重遵循汇合超几何分布的贝塔分布的混合。从汇合超几何分布中采样时，采用了一种浓缩的查表方法。理论分析研究了构建浓缩查找表所需的计算量。通过数值实验，我们证明了当从同一分布生成大量伪随机向量时，所提出的算法优于基于拒绝的方法。
期刊介绍：
Statistics and Computing is a bi-monthly refereed journal which publishes papers covering the range of the interface between the statistical and computing sciences.
In particular, it addresses the use of statistical concepts in computing science, for example in machine learning, computer vision and data analytics, as well as the use of computers in data modelling, prediction and analysis. Specific topics which are covered include: techniques for evaluating analytically intractable problems such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation, search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification.
In addition, the journal contains original research reports, authoritative review papers, discussed papers, and occasional special issues on particular topics or carrying proceedings of relevant conferences. Statistics and Computing also publishes book review and software review sections.
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