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Spatial Gaussian process regression models typically contain finitedimensional covariance parameters that need to be estimated from the data. Westudy the Bayesian estimation of covariance parameters including the nuggetparameter in a general class of stationary covariance functions underfixed-domain asymptotics, which is theoretically challenging due to theincreasingly strong dependence among spatial observations. We propose a noveladaptation of the Schwartz's consistency theorem for showing posteriorcontraction rates of the covariance parameters including the nugget. We derivea new polynomial evidence lower bound, and propose consistent higher-orderquadratic variation estimators that satisfy concentration inequalities withexponentially small tails. Our Bayesian fixed-domain asymptotics theory leadsto explicit posterior contraction rates for the microergodic and nuggetparameters in the isotropic Matern covariance function under a generalstratified sampling design. We verify our theory and the Bayesian predictiveperformance in simulation studies and an application to sea surface temperaturedata.

Fixed-domain Posterior Contraction Rates for Spatial Gaussian Process Model with Nugget