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.