{"title":"Perfect Sampling of the Posterior in the Hierarchical Pitman-Yor Process.","authors":"S. Bacallado, S. Favaro, Samuel Power, L. Trippa","doi":"10.1214/21-BA1269","DOIUrl":null,"url":null,"abstract":"The predictive probabilities of the hierarchical Pitman-Yor process are approximated through Monte Carlo algorithms that exploits the Chinese Restaurant Franchise (CRF) representation. However, in order to simulate the posterior distribution of the hierarchical Pitman-Yor process, a set of auxiliary variables representing the arrangement of customers in tables of the CRF must be sampled through Markov chain Monte Carlo. This paper develops a perfect sampler for these latent variables employing ideas from the Propp-Wilson algorithm and evaluates its average running time by extensive simulations. The simulations reveal a significant dependence of running time on the parameters of the model, which exhibits sharp transitions. The algorithm is compared to simpler Gibbs sampling procedures, as well as a procedure for unbiased Monte Carlo estimation proposed by Glynn and Rhee. We illustrate its use with an example in microbial genomics studies.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.9000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bayesian Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/21-BA1269","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 1
Abstract
The predictive probabilities of the hierarchical Pitman-Yor process are approximated through Monte Carlo algorithms that exploits the Chinese Restaurant Franchise (CRF) representation. However, in order to simulate the posterior distribution of the hierarchical Pitman-Yor process, a set of auxiliary variables representing the arrangement of customers in tables of the CRF must be sampled through Markov chain Monte Carlo. This paper develops a perfect sampler for these latent variables employing ideas from the Propp-Wilson algorithm and evaluates its average running time by extensive simulations. The simulations reveal a significant dependence of running time on the parameters of the model, which exhibits sharp transitions. The algorithm is compared to simpler Gibbs sampling procedures, as well as a procedure for unbiased Monte Carlo estimation proposed by Glynn and Rhee. We illustrate its use with an example in microbial genomics studies.
期刊介绍：
Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining.
Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.
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