{"title":"Efficient sampling from the PKBD distribution","authors":"Lukas Sablica, Kurt Hornik, Josef Leydold","doi":"10.1214/23-ejs2149","DOIUrl":null,"url":null,"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.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/23-ejs2149","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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.
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.