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Activity Number: 168 - Bayesian Models for Gaussian and Point Processes
Type: Contributed
Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #323720
Title: Bayesian Gaussian Process Models on Spaces of Sufficient Dimension Reduction
Author(s): Peter Marcy*
Companies: Los Alamos National Laboratory
Keywords: computer experiment ; MCMC ; Grassmannian manifold ; Stiefel manifold ; sensitivity analysis ; gradients
Abstract:

It is often known that important directions within the input space of Gaussian process (GP) regression models do not align with the original coordinate directions. It might be the case that changes along unknown linear combinations of the inputs effect the biggest changes in the response variables. There are two goals associated with this GP model: (1) the usual goal of in-fill prediction, i.e. "emulation", and (2) inferring a sufficient dimension reduction space, along with uncertainty of the linear combinations. In this talk I present a Bayesian formulation of the problem and describe the challenges to inference. I then describe a general Metropolis-Hastings algorithm for exploring the posterior, which is known to lie on a Stiefel manifold. The methodology is illustrated using data from a complex computer model.


Authors who are presenting talks have a * after their name.

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