Nonparametric Bayes inference on conditional independence

• 成果类型: Article
• 署名作者: Kunihama, Tsuyoshi; Dunson, David B.
• 署名单位: University of Washington; University of Washington Seattle; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv060
• 发表日期: 2016
• 页码: 3547
• 关键词: mixtures; association; definition

摘要

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 singleMarkov 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.