Publication Date:
2016-03-01
Description:
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.
Print ISSN:
0006-3444
Electronic ISSN:
1464-3510
Topics:
Biology
,
Mathematics
,
Medicine
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