Perfect Sampling of the Posterior in the Hierarchical Pitman-Yor Process.

IF 4.9 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Bayesian Analysis Pub Date : 2021-01-01 DOI:10.1214/21-BA1269

S. Bacallado, S. Favaro, Samuel Power, L. Trippa

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.

查看原文本刊更多论文

分层Pitman-Yor过程中后验的完美抽样。

分层Pitman-Yor过程的预测概率通过蒙特卡罗算法进行近似，该算法利用中餐馆特许经营(CRF)表示。然而，为了模拟分层Pitman-Yor过程的后验分布，必须通过马尔可夫链蒙特卡罗对一组表示CRF表中客户排列的辅助变量进行采样。本文利用Propp-Wilson算法的思想开发了一种针对这些潜在变量的完美采样器，并通过大量的仿真评估了其平均运行时间。仿真结果表明，运行时间对模型参数有显著的依赖性，模型参数具有明显的过渡。该算法与更简单的Gibbs抽样程序以及由Glynn和Rhee提出的无偏蒙特卡罗估计程序进行了比较。我们用一个微生物基因组学研究的例子来说明它的使用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Bayesian Analysis 数学-数学跨学科应用

CiteScore

6.50

自引率

13.60%

发文量

审稿时长

>12 weeks

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.