A Bayesian nonparametric approach to testing for dependence between random variables

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Title: A Bayesian nonparametric approach to testing for dependence between random variables
Authors: Filippi, S
Holmes, C
Item Type: Journal Article
Abstract: Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity assumptions implicit in traditional association scores such as correlation. Here we describe a Bayesian nonparametric procedure that leads to a tractable, explicit and analytic quantification of the relative evidence for dependence vs independence. Our approach uses Polya tree priors on the space of probability measures which can then be embedded within a decision theoretic test for dependence. Polya tree priors can accommodate known uncertainty in the form of the underlying sampling distribution and provides an explicit posterior probability measure of both dependence and independence. Well known advantages of having an explicit probability measure include: easy comparison of evidence across different studies; encoding prior information; quantifying changes in dependence across different experimental conditions, and; the integration of results within formal decision analysis.
Issue Date: 21-Sep-2016
Date of Acceptance: 1-Aug-2016
URI: http://hdl.handle.net/10044/1/43899
DOI: https://dx.doi.org/10.1214/16-BA1027
ISSN: 1931-6690
Publisher: International Society for Bayesian Analysis (ISBA)
Start Page: 919
End Page: 938
Journal / Book Title: Bayesian Analysis
Volume: 12
Issue: 4
Copyright Statement: © 2016 International Society for Bayesian Analysis
Keywords: Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Statistics & Probability
dependence measure
Bayesian nonparametrics
Polya tree
hypothesis testing
0104 Statistics
Publication Status: Published
Appears in Collections:Faculty of Medicine
Epidemiology, Public Health and Primary Care

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