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- Title
Nonparametric Bayes inference on conditional independence.
- Authors
TSUYOSHI KUNIHAMA; DUNSON, DAVID B.
- 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.
- Subjects
DIRICHLET forms; EMPIRICAL Bayes methods; BAYESIAN analysis; GRAPHICAL modeling (Statistics); GRAPHIC methods for multivariate analysis; CRIMINOLOGY
- Publication
Biometrika, 2016, Vol 103, Issue 1, p35
- ISSN
0006-3444
- Publication type
Article
- DOI
10.1093/biomet/asv060