Prior and Prejudice: An Algorithm for Weakening Prior Influence

• Activity Number: 503
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Keli Liu*+ and Xiao-Li Meng and Natesh S. Pillai
• Companies: and Harvard and Harvard
• Keywords: objective prior ; weakly informative ; Jeffreys ; Frequentist calibration

Abstract

Prejudice leads to inequality. A prior favoring select models over others leads to Bayes procedures that perform better under the favored models. This intuition forms the foundation for our prior weakening algorithm: iteratively reweight our initial prior until the resulting Bayes procedures perform uniformly well across the parameter space. We implement this idea when uniform coverage of posterior intervals at a fixed significance level is desired. The practitioner begins with any non-dogmatic prior and applies the algorithm iteratively to obtain a sequence of progressively weaker priors, with progressively better coverage properties. The limit is an objective prior. In practice, prior influence can play a valuable role in regularizing the model. Since we provide not just an objective prior, but a sequence of progressively weaker priors, a practitioner can weigh the benefits of regularization against that of uniform performance. Asymptotically (in sample size), our algorithm converges to the uniform (discrete parameter) and Jeffreys (continuous parameter) priors. In finite samples, our algorithm automatically adjusts these limiting priors to ensure better coverage properties.