Math @ Duke

Publications [#322543] of David B. Dunson
search arxiv.org.Papers Published
 Kunihama, T; Dunson, DB, Nonparametric Bayes inference on conditional independence,
Biometrika, vol. 103 no. 1
(January, 2015),
pp. 3547, Oxford University Press (OUP) [doi]
(last updated on 2019/05/26)
Abstract: © 2016 Biometrika Trust. 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 decisiontheoretic 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.


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