Bayesian Semiparametric Covariance Function Estimation for Stationary Gaussian Processes by Overwhelming Force

Restricted (Penn State Only)
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
  • 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.