Bayesian Optimal Sequential Design for Random Function Estimation

• Activity Number: 123
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Marco A. R. Ferreira*+
• Companies: University of Missouri
• Keywords: Bayesian analysis ; EMCMC ; expected utility maximization ; simulation-based algorithms

Abstract

We develop a novel computational framework for Bayesian optimal sequential design for random function estimation. This computational framework is based on evolutionary Markov chain Monte Carlo, which combines ideas of genetic or evolutionary algorithms with the power of Markov chain Monte Carlo. Our framework is able to consider general models for the observations, such as exponential family distributions and scale mixtures of normals. In addition, our framework allows optimality criteria with general utility functions that may include competing objectives, such as for example minimization of costs, minimization of the distance between true and estimated functions, and minimization of the prediction error. Finally, we illustrate our novel methodology with applications to design of a computer model experiment and experimental design for nonparametric function estimation.