Frequency of Frequencies Distributions and Size-Dependent Exchangeable Random Partitions

• 成果类型: Article
• 署名作者: Zhou, Mingyuan; Favaro, Stefano; Walker, Stephen G.
• 署名单位: University of Texas System; University of Texas Austin; University of Turin; Collegio Carlo Alberto; University of Texas System; University of Texas Austin; University of Texas System; University of Texas Austin
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1222290
• 发表日期: 2017
• 页码: 1623-1635
• 关键词: dirichlet processes; disclosure risk; rna-seq; models; Microdata; population; priors; COUNT; LAW

摘要

Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this article introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions. A cluster structure, naturally arising from a completely random measure mixed Poisson process, allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size, a distinct and motivated feature that makes it more flexible than a partition structure. This allows it to model an entire FoF distribution whose structural properties change as the population size varies. An FoF vector can be simulated by drawing an infinite number of Poisson random variables, or by a stick-breaking construction with a finite random number of steps. A generalized negative binomial process model is proposed to generate a cluster structure, where in the prior the number of clusters is finite and Poisson distributed, and the cluster sizes follow a truncated negative binomial distribution. We propose a simple Gibbs sampling algorithm to extrapolate the FoF vector of a population given the FoF vector of a sample taken without replacement from the population. We illustrate our results and demonstrate the advantages of the proposed models through the analysis of real text, genomic, and survey data. Supplementary materials for this article are available online.