@article{Filippi:2017:10.1214/16-BA1027,
author = {Filippi, S and Holmes, C},
doi = {10.1214/16-BA1027},
journal = {Bayesian Analysis},
pages = {919--938},
title = {A Bayesian nonparametric approach to testing for dependence between  random variables},
url = {http://dx.doi.org/10.1214/16-BA1027},
volume = {12},
year = {2017}
}

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TY  - JOUR
AB  - Nonparametric and nonlinear measures of statistical dependence between pairsof random variables are important tools in modern data analysis. In particularthe emergence of large data sets can now support the relaxation of linearityassumptions 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 vsindependence. Our approach uses Polya tree priors on the space of probabilitymeasures which can then be embedded within a decision theoretic test fordependence. Polya tree priors can accommodate known uncertainty in the form ofthe underlying sampling distribution and provides an explicit posteriorprobability measure of both dependence and independence. Well known advantagesof having an explicit probability measure include: easy comparison of evidenceacross different studies; encoding prior information; quantifying changes independence across different experimental conditions, and; the integration ofresults within formal decision analysis.
AU  - Filippi,S
AU  - Holmes,C
DO  - 10.1214/16-BA1027
EP  - 938
PY  - 2017///
SN  - 1931-6690
SP  - 919
TI  - A Bayesian nonparametric approach to testing for dependence between  random variables
T2  - Bayesian Analysis
UR  - http://dx.doi.org/10.1214/16-BA1027
UR  - http://hdl.handle.net/10044/1/43899
VL  - 12
ER  - 

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