Evolutionary Markov Chain Monte Carlo Algorithms for Bayesian Optimal Sequential Design

• Activity Number: 250
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Marco Ferreira*+
• Companies: University of Missouri
• Keywords: EMCMC ; genetic operators ; splines ; Gaussian processes

Abstract

We present evolutionary Markov chain Monte Carlo (EMCMC) algorithms for Bayesian optimal sequential design. These algorithms combine genetic or evolutionary operators with the flexibility of Markov chain Monte Carlo. A salient feature of these algorithms is that they are able to accommodate observations in the exponential family of distributions and in the class of scale mixtures of normals. Furthermore, they are able to accommodate 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 experimental design for nonparametric function estimation and to network design for the study of spatiotemporal processes.