The Nonparametric Bayesian Model with Shrinkage Priors and Its Application in Multiple Pesticide Exposures Data

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ran Wei* and Subhashis Ghoshal and Brian J. Reich
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Nonparametric ; Bayesian ; Shinkage ; Multiple exposures

Abstract

Choosing an appropriate subset of variables related to the outcome measurements is one of the important steps in studying the overall effects of multiple factors on individual outcomes. We propose a Bayesian nonparametric regression model with multivariate shrinkage priors for variable selection and model prediction. This regression model first reduces the nonparametric regression function to additive linear settings by basis expansion in a way that each chemical main effect and interaction effect is associated with a basis function and coefficient vector. The multivariate horseshoe priors are imposed to shrink the coefficients of trivial variables. An auxiliary thresholding step can then discard these variables while keeping the important variables. This model is applied in the multiple pesticide exposures data to select a subset of pesticide chemicals associated with human neurobehavioral measurement, as well as predicting the thresholding level of pesticide exposures. The simulation study has demonstrated the advantages of our method in variable selection and model prediction in terms of false positives, false negatives as well as prediction mean squared errors.