Blended Paradigm Inference

• Activity Number: 497
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Steven MacEachern*+ and Yoonkyung Lee and John Lewis
• Companies: The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: Bayesian ; Robust Inference ; Outliers

Abstract

Blended paradigm inference seeks to combine complementary aspects of classical and Bayesian inference. Classical estimators, while model-based, are often designed to exhibit robustness to model misspecification. In contrast, Bayesian methods hubristically claim to model every aspect of the data-generation process. The blended paradigm relies on a Bayesian argument. A model is posited for the data, and the model is used to pass from prior distribution to posterior distribution. However, only a portion of the likelihood is used for the update. The likelihood used for updating is that of a classical statistic under the posited model. The remaining portion of the likelihood is discarded. This talk will motivate the blended paradigm and will illustrate a number of properties of specific implementations. With a sound choice of summary statistics, the method performs nearly as well as the traditional Bayesian update when the posited model holds and peforms much better when the posited model strays from the truth.