Bayesian Computation Using Design of Experiments-Based Interpolation Technique

Abstract

In this article, a new deterministic approximation method for Bayesian computation, known as design of experiments-based interpolation technique (DoIt), is proposed. The method works by sampling points from the parameter space using an experimental design and then fitting a kriging model to interpolate the unnormalized posterior. The approximated posterior density is a weighted average of normal densities, and therefore, most of the posterior quantities can be easily computed. DoIt is a general computing technique that is easy to implement and can be applied to many complex Bayesian problems. Moreover, it does not suffer from the curse of dimensionality as much as some quadrature methods. It can work using fewer posterior evaluations, which is a great advantage over the Monte Carlo and Markov chain Monte Carlo methods, especially when dealing with computationally expensive posteriors. This article has supplementary material that is available online.

KEY WORDS:

• Computer experiments
• Experimental design
• Kriging
• Laplace’s method

ACKNOWLEDGMENTS

The author thanks the editor, four referees, and Mr. Rui Tuo for their valuable comments and suggestions. This research was supported by the U.S. National Science Foundation grant CMMI-1030125.