Bayesian Functional Data Analysis for Computer Model Validation

GUEST LECTURER
Fei Liu: Faculty candidate

AFFILIATION
Duke University

ABSTRACT
Functional data analysis (FDA) -- inference on curves or functions -- has wide application in statistics. An example of considerable recent interest arises when considering computer models of processes; the output of such models is a function over the space of inputs of the computer model. The output is functional data in many contexts, such as when the output is a function of time, a surface, etc. A nonparametric Bayesian statistics approach, utilizing separable Gaussian Stochastic Process as the prior distribution for functions, is a natural choice for smooth functions in a manageable (time) dimension. However, direct use of separable Gaussian stochastic processes is inadequate for irregular functions, and can be computationally infeasible in high dimensional cases. In this talk, we will develop and extend several Bayesian FDA approaches for high dimensional irregular functions in the context of computer model validation, tailored to interdisciplinary problems in engineering and the environment.