A0236
Title: Bayesian fixed-domain asymptotics for covariance parameters in spatial Gaussian process models
Authors: Cheng Li - National University of Singapore (Singapore) [presenting]
Saifei Sun - City University of Hong Kong (Hong Kong)
Yichen Zhu - Duke University (United States)
Abstract: Gaussian process models typically contain finite dimensional parameters in the covariance function that need to be estimated from the data. The Bayesian fixed-domain asymptotics is studied for the covariance parameters in spatial Gaussian process regression models with an isotropic Matern covariance function, which has many applications in spatial statistics. For the model without nugget, it is shown that when the dimension of the domain is less than or equal to three, the microergodic parameter and the range parameter are asymptotically independent in the posterior. While the posterior of the microergodic parameter is asymptotically close in total variation distance to a normal distribution with shrinking variance, the posterior distribution of the range parameter does not converge to any point mass distribution in general. New evidence for the model with nugget is derived from lower bound and consistent higher-order quadratic variation estimators, which lead to explicit posterior contraction rates for both the micro ergodic and nugget parameters. The asymptotic efficiency and convergence rates of Bayesian kriging prediction are further studied. All the new theoretical results are verified in numerical experiments and real data analysis.
