Ratio-of-Uniforms Markov Chain Monte Carlo for Gaussian Process Models

Open Access
Author:
Groendyke, Christophe
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
None
Committee Members:
  • David Russell Hunter, Thesis Advisor/Co-Advisor
  • Murali Haran, Thesis Advisor/Co-Advisor
Keywords:
  • spatial statistics
  • Markov chain Monte Carlo
  • auxiliary variable methods
  • ratio of uniforms
Abstract:
We develop various Markov chain Monte Carlo(MCMC) methods based on the ratio-of-uniforms (ROU) transformation and show how they can be used in a Bayesian context to simulate from the posterior distribution of linear Gaussian process models. These models are very popular in many disciplines, but are particularly important for modeling spatial data. We show that these algorithms, in spite of requiring no tuning, perform well in practice. We describe how the algorithms can be used in conjunction with some recently developed methods to estimate standard errors of MCMC-based estimates accurately. The estimated standard errors can, in turn, be used to automatically decide when to stop the MCMC runs thereby providing, in principle, a completely automated MCMC algorithm. We conclude with a study of the properties of these algorithms, using simulated as well as real data, taken from the field of Geosciences.