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2016 Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures
Sarah Filippi, Chris C. Holmes, Luis E. Nieto-Barajas
Electron. J. Statist. 10(2): 3338-3354 (2016). DOI: 10.1214/16-EJS1171

Abstract

In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a “null model” of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets.

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Sarah Filippi. Chris C. Holmes. Luis E. Nieto-Barajas. "Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures." Electron. J. Statist. 10 (2) 3338 - 3354, 2016. https://doi.org/10.1214/16-EJS1171

Information

Received: 1 December 2015; Published: 2016
First available in Project Euclid: 16 November 2016

zbMATH: 1358.62058
MathSciNet: MR3572852
Digital Object Identifier: 10.1214/16-EJS1171

Keywords: Bayes nonparametrics , Contingency table , dependence measure , Hypothesis testing , mixture model , mutual information

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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