A Bayesian nonparametric approach to testing for dependence between
random variables
random variables
File(s)
Published version
Author(s)
Filippi, S
Holmes, C
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.
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.
Date Issued
2017-12-01
Date Acceptance
2016-08-01
Citation
Bayesian Analysis, 2017, 12 (4), pp.919-938
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
Subjects
stat.ME
stat.ME
Publication Status
Published
Date Publish Online
2016-09-21