A0286
Title: Bayesian fixed-domain posterior contraction for spatial Gaussian process model with nugget
Authors: Cheng Li - National University of Singapore (Singapore) [presenting]
Saifei Sun - City University of Hong Kong (Hong Kong)
Yichen Zhu - Bocconi University (Italy)
Abstract: Spatial Gaussian process regression models typically contain finite dimensional covariance parameters that need to be estimated from the data. The Bayesian estimation of covariance parameters is studied, including the nugget parameter in a general class of stationary covariance functions under fixed-domain asymptotics, which is theoretically challenging due to the increasingly strong dependence among spatial observations. A novel adaptation of Schwartz's consistency theorem is proposed for showing posterior contraction rates of the covariance parameters, including the nugget. A new polynomial evidence lower bound is derived, and consistent higher-order quadratic variation estimators are proposed that satisfy concentration inequalities with exponentially small tails. The Bayesian fixed-domain asymptotics theory leads to explicit posterior contraction rates for the microergodic and nugget parameters in the isotropic Matern covariance function under a general stratified sampling design. The theory and the Bayesian predictive performance are verified in simulation studies and an application to sea surface temperature data.
