Model Mining: A Case Study in Air Pollution and Mortality

• Activity Number: 492
• Type: Contributed
• Date/Time: Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ciprian Crainiceanu*+
• Companies: Johns Hopkins University
• Keywords: Model Uncertainty ; Air pollution ; Health effects ; Bayes factors ; BIC ; BMA

Abstract

Current studies of health effects of air pollution routinely use up to 15 years of daily observations for as many as 100 cities and numerous covariates. This research is part of a new trend in statistics being shaped by the availability of large databases containing millions of observations and hundreds or thousands of covariates. We propose and implement model mining, a new model sensitivity procedure designed to answer the question does X affect Y? This procedure identifies the maximum likelihood model within the class of regression models with X and W as covariates and exactly k additional covariates chosen from an available set U. We report the likelihood for each such model together with a fixed-level confidence interval for the parameter of X. While theoretically appealing, Bayesian Model Averaging requires Bayes factors calculation, which tends to be computationally prohibitive for complex models and large datasets. Moreover, in linear regression, we show the Bayes factors are practically equivalent to an information criterion with a penalty depending on the prior. The serious limitations of BMA in the context of policymaking are discussed.