Secure Bayesian Model Averaging for Horizontally Partitioned Data

• Activity Number: 168
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Joyee Ghosh*+ and Jerome P. Reiter
• Companies: University of Iowa and Duke University
• Keywords: Bayesian model averaging ; Data confidentiality ; Disclosure limitation ; Markov chain Monte Carlo ; Variable selection

Abstract

The Bayesian paradigm allows one to incorporate covariate set uncertainty in linear regression and its generalizations by considering models corresponding to all possible combinations of covariates. Depending on the goals of the study, posterior probabilities of models can be used for model selection or model averaging. The setting in which multiple data owners or agencies possess data on different subjects but the same set of covariates is known as horizontally partitioned data. Such owners are often interested in global inference or prediction using Bayesian model averaging (BMA) for the combined data. However, sharing data across agencies may be infeasible for confidentiality issues. For linear regression, we introduce an approach called secure Bayesian model averaging (BMA), which performs exact BMA for the combined data without sharing information on individual subjects, using a technique called secure summation. For binary regression we first describe an exact approach to BMA, which requires several rounds of secure summation. As an alternative, we also suggest an approximate approach which requires only one round of secure summation, as in the case of linear regression.