Lizhen Lin - Duke University

4:00 pm on Monday, January 27, 2014
5:00 pm on Monday, January 27, 2014
MCS 137
Title: Shape constrained regression using Gaussian process projections. Abstract: Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid implausible results. In this talk, I will talk about nonparametric methods for estimating shape constrained (mainly monotone constrained) regression functions. I will focus on a novel Bayesian method from our recent work for estimating monotone curves and surfaces using Gaussian process projections. Inference is based on projecting posterior samples from the Gaussian process. Theory is developed on continuity of the projection and rates of contraction. Our approach leads to simple computation with good performance in finite samples. The projection approach can be applied in other constrained function estimation problems including in multivariate settings.