Nonparametric Bayes inference on conditional independence
Journal Article (Journal Article)
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.
Full Text
Duke Authors
Cited Authors
- Kunihama, T; Dunson, DB
Published Date
- January 1, 2015
Published In
Volume / Issue
- 103 / 1
Start / End Page
- 35 - 47
Electronic International Standard Serial Number (EISSN)
- 1464-3510
International Standard Serial Number (ISSN)
- 0006-3444
Digital Object Identifier (DOI)
- 10.1093/biomet/asv060
Citation Source
- Scopus