Statistics Papers

Document Type

Journal Article

Date of this Version

2004

Publication Source

Journal of Computational and Graphical Statistics

Volume

13

Issue

1

Start Page

1

Last Page

19

DOI

10.1198/1061860043119

Abstract

This article describes how a mixture of two densities, f0 and f1, may be decomposed into a different mixture consisting of three densities. These new densities, f+, f, and f=, summarize differences between f0 and f1: f+ is high in areas of excess of f1 compared to f0; f represents deficiency of f1 compared to f0 in the same way; f= represents commonality between f1 and f0. The supports of f+ and f are disjoint. This decomposition of the mixture of f0 and f1 is similar to the set-theoretic decomposition of the union of two sets A and B into the disjoint sets A\B, B\A, and AB. Sample points from f0 and f1 can be assigned to one of these three densities, allowing the differences between f0 and f1 to be visualized in a single plot, a visual hypothesis test of whether f0 is equal to f1. We describe two similar such decompositions and contrast their behavior under the null hypothesis f0 = f1, giving some insight into how such plots may be interpreted. We present two examples of uses of these methods: visualization of departures from independence, and of a two-class classification problem. Other potential applications are discussed.

Keywords

classification, data visualization, density estimation, exploratory data analysis, mixture decomposition

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Date Posted: 27 November 2017

This document has been peer reviewed.