Estimating Shape Constrained Functions Using Gaussian Processes

Xiaojing Wang
Department of Statistics
University of Connecticut

ABSTRACT:
Gaussian processes are a popular tool for nonparametric function estimation because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. Often, however, the function is known to be in a shape-constrained class, such as the class of monotonic functions or convex functions. For Gaussian processes with squared exponential correlation function, shape constraints can be incorporated through the use of derivative processes, which are joint Gaussian processes with the original process. The extent to which this is feasible is discussed, and illustrated through simulated examples and an example involving emulating a computer model of crashworthiness. Computation is carried out through a Gibbs sampling scheme.