Estimating Shape Constrained Functions Using Gaussian Processes (Xiaojing Wang-University of Connecticut)

4:00 pm on Thursday, October 18, 2018
5:00 pm on Thursday, October 18, 2018
MCS 148, 111 Cummington Mall
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, the function is known to be in a shape-constrained class, such as the class of monotonic or convex functions. Such shape constraints can be incorporated through the use of derivative processes, which are joint Gaussian processes with the original process, as long as the conditions of mean square differentiability hold. The possibilities and challenges of introducing shape constraints through this device are explored, and illustrated through simulations and two real data examples. Computation is carried out through a Gibbs sampling scheme. Joint work with Jim Berger, Duke University