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Activity Number: 175 - Bayesian Theory, Foundations, and Nonparametrics
Type: Contributed
Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #329088 Presentation
Title: Posterior Convergence and Coverage Aspects of Gaussian Process Approximations
Author(s): Biraj Subhra Guha* and Debdeep Pati
Companies: Texas A & M University and Texas A&M University
Keywords: Gaussian Processes; Posterior Convergence; High Dimension

In this talk we study theoretical properties low rank decompositions of Gaussian process, which are frequently used in spatial statistics to mitigate numerical issues arising from inversion of high dimensional covariance matrices. We develop general conditions on the low rank decomposition so that the posterior converges at the minimax rate and credible intervals achieve nominal level asymptotically. We specialize to a particular low rank approximation obtained from spectral decomposition, and demonstrate empirically that it achieves better coverage properties compared to existing approaches of approximating Gaussian processes.

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

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