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Nonparametric Bayes inference on conditional independence

Authors :
Tsuyoshi Kunihama
David B. Dunson
Publication Year :
2014
Publisher :
arXiv, 2014.

Abstract

In many application areas, a primary focus is on assessing evidence in the data refuting the assumption of independence of $Y$ and $X$ conditionally on $Z$, with $Y$ response variables, $X$ predictors of interest, and $Z$ covariates. Ideally, one would have methods available that avoid parametric assumptions, allow $Y, X, Z$ to be random variables on arbitrary spaces with arbitrary dimension, and accommodate rapid consideration of different candidate predictors. As a formal decision-theoretic approach has clear disadvantages in this context, we instead rely on an encompassing nonparametric Bayes model for the joint distribution of $Y$, $X$ and $Z$, with conditional mutual information used as a summary of the strength of conditional dependence. We construct a functional of the encompassing model and empirical measure for estimation of conditional mutual information. The implementation relies on a single Markov chain Monte Carlo run under the encompassing model, with conditional mutual information for candidate models calculated as a byproduct. We provide an asymptotic theory supporting the approach, and apply the method to variable selection. The methods are illustrated through simulations and criminology applications.

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....dd6152b17f0cc133fe35d55cbabd9c22
Full Text :
https://doi.org/10.48550/arxiv.1404.1429