A review of multivariate distributions for count data derived from the Poisson distribution. (28th March 2017)

• Record Type: Journal Article
• Authors: Inouye, David I.; Yang, Eunho; Allen, Genevera I.; Ravikumar, Pradeep
• Is Part Of: Wiley interdisciplinary reviews. Volume 9:Number 3(2017)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-03-28
• Subjects: Poisson -- Multivariate -- Graphical models -- Copulas -- High dimensional; Mathematical statistics -- Data processing -- Periodicals; Science -- Data processing -- Periodicals; Social sciences -- Data processing -- Periodicals; Mathematical statistics -- Periodicals; 519.50285
• DOI: 10.1002/wics.1398
• Languages: English
• ISSNs: 1939-5108

Abstract

Abstract : The Poisson distribution has been widely studied and used for modeling univariate count‐valued data. However, multivariate generalizations of the Poisson distribution that permit dependencies have been far less popular. Yet, real‐world, high‐dimensional, count‐valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: (1) where the marginal distributions are Poisson, (2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and (3) where the node‐conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real‐world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent Discussion section. WIREs Comput Stat 2017, 9:e1398. doi: 10.1002/wics.1398 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Abstract : This paper reviews and empirically compares multivariate models derived from the Poisson distribution which can be categorized into three model classes based on primary modeling assumptions.