Multivariate normal (MVN) probabilities are needed in the model estimation and posterior inference for several important extensions of the classic Gaussian process (GP). They are analytically intractable and need to be evaluated through Monte-Carlo-based numerical integration. We discover that the dominant complexity for the classic separation-of-variable (SOV) and minimax exponential tilting (MET) methods for the numerical evaluation of MVN probabilities comes from the computation of the conditional mean and variance of the integration variables.

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Speaker Biography: Dr. Cao is an assistant professor specialized in Computational and Spatial Statistics in the Department of Mathematics at The University of Houston. He obtained the Ph.D. degree in Statistics at King Abdullah University of Science and Technology (KAUST), advised by Dr. Marc Genton. Prior to that, he obtained a B.S. in Mathematics from University of Science and Technology of China. Cao’s broad research interests lie on scalable computational methods for statistical machine learning. During his postdoc at Texas A&M, he worked on scalable Gaussian process regression and variable selection, transport maps, and variational Bayes, most of which are based on the Vecchia approximation of Gaussian processes. His research is mostly related to applications in spatial statistics, climate science, and agricultural science.