Nonparametric Bayes inference on conditional independence

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.

Duke Scholars

Author David B. Dunson Statistical Science