Bayesian Semiparametric Covariance Function Estimation for Stationary Gaussian Processes by Overwhelming Force
Open Access
Author:
Ensley, John Robert
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
November 16, 2017
Committee Members:
Benjamin Adam Shaby, Thesis Advisor/Co-Advisor David Russell Hunter, Committee Member Ephraim Mont Hanks, Committee Member
Keywords:
Gaussian process bayesian covariance function mcmc parallel computing penalized splines spectral density monte carlo integration semiparametric
Abstract:
We use a fully Bayesian framework to semiparametrically estimate covariance
functions of stationary Gaussian processes from irregularly-spaced data. The
covariance functions are modeled in the spectral domain on the log-log scale using
penalized natural splines, which results in a flexible class of smooth densities that
have power law tails. The Fourier transforms required to construct likelihoods from
the spectral densities are computed using standard Monte Carlo integration. These
calculations require massive computational effort, but are highly parallelizable. By
utilizing GPUs, computational speeds are competitive with standard parametric
covariance model estimation.