A Composite Likelihood Approach for Computer Experiments

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Ximing Xu*+ and Derek Bingham and Nancy Reid
• Companies: University of Toronto and Simon Fraser University and University of Toronto
• Keywords: computer experiment ; composite lilkelihood ; universal kriging ; Gaussian process

Abstract

Modeling the computer outputs as a sample path of a Gaussian process has proven useful to predict the outputs at untried input sites. However as the number of simulator evaluations gets larger, statistically modeling the computer outputs usually becomes computationally intractable. In this paper we model the mean of the Gaussian process as a regression function of the input vector and estimate the unknown parameters based on the pairwise likelihood of the high dimensional Gaussian distribution. We also derive a new method to do prediction by maximizing a special composite likelihood. The composite likelihood approach does not need to calculate the inverse or determinant of the high dimensional covariance matrix and require fewer model assumptions and much less computation time than full likelihood based methods. Finally our approach is applied to analyze a real photometric redshift data and performs very well in predictive accuracy.