**CANCELLED DUE TO WEATHER**

The seminar will be rescheduled soon

SHAPE CONSTRAINED
REGRESSION USING
GAUSSIAN PROCESS
PROJECTIONS

Lizhen Lin, Duke University
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.