Making Robust Decisions with Approximate Models in Complex Data Domains

• Activity Number: 395
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Chris Holmes*
• Companies: University of Oxford

Abstract

Conventional Bayesian decision analysis assumes a perfectly specified loss function and a precisely specified model. In practice both of these elements are tentative and approximations are used. A key concern then is how to judge the sensitivity of decisions to the unknown model misspecification. In an era of "big-data" where statisticians are increasingly having to utilise approximate models by design there is a pressing need to re-visit formal methods for studying decision robustness. We describe recent work in nonparametric computational Bayesian decision theory, motivated by problems in biomedical genomics, that provides a formal framework to achieve this. In particular we show how to compute the local minimax loss and variation on expected loss for all distributions (models) within a small Kullback-Leibler (KL) neighbourhood around the approximating model. We show that KL is the only coherent divergence criteria that can be used, and we describe efficient Monte Carlo methods for achieving robust analysis, including graphical methods for decision sensitivity analysis.