论文标题
空间高斯工艺模型的固定域后部收缩率
Fixed-domain Posterior Contraction Rates for Spatial Gaussian Process Model with Nugget
论文作者
论文摘要
空间高斯过程回归模型通常包含有限维度协方差参数，需要从数据估算。我们研究了在固定域渐进剂中，贝叶斯对协方差参数的估计，包括一般的固定协方差函数中的掘金参数，这在理论上在空间观察中越来越强大，因此在理论上具有挑战性。我们提出了Schwartz一致性定理的新颖适应性，用于显示包括掘金在内的协方差参数的后部收缩率。我们得出了一个新的多项式证据，并提出了一致的高阶二次变异估计器，该估计值满足浓度不平等的尾巴呈指数小的尾巴。我们的贝叶斯固定域渐近学理论导致在一般分层抽样设计下，各向同性孕妇协方差功能的微能和掘金参数显式后部收缩率。我们在模拟研究中验证我们的理论和贝叶斯预测性能，并应用于海面温度数据。
Spatial Gaussian process regression models typically contain finite dimensional covariance parameters that need to be estimated from the data. We study the Bayesian estimation of covariance parameters 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. We propose a novel adaptation of the Schwartz's consistency theorem for showing posterior contraction rates of the covariance parameters including the nugget. We derive a new polynomial evidence lower bound, and propose consistent higher-order quadratic variation estimators that satisfy concentration inequalities with exponentially small tails. Our 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. We verify our theory and the Bayesian predictive performance in simulation studies and an application to sea surface temperature data.
