Spring 2015
Seminars are held on Thursdays in Cullimore Hall. For questions about the seminar schedule, please contact Antai Wang.
Date: April 2, 2015
Speaker: Bin Zhu
National Cancer Institute DCEG, Biostatistics Branch,
National Institutes of Health
Title: "Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes"
Abstract:
We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's mth-order derivative. The nesting comes in through including a local instantaneous mean function, which is drawn from another Gaussian process inducing adaptivity to locally-varying smoothness. We discuss the support of the nGP prior in terms of the closure of a reproducing kernel Hilbert space,and consider theoretical properties of the posterior. The posterior mean under the nGP prior is shown to be equivalent to the minimizer of a nested penalized sum-of-squares involving penalties for both the global and local roughness of the function. Using highly-efficient Markov chain Monte Carlo for posterior inference, the proposed method performs well in simulation studies compared to several alternatives, and is scalable to massive data, illustrated through a proteomics application.