Spatial-temporal data requires flexible regression models which can model the dependence of responses on space- and time-dependent covariates. In this paper, we describe a semiparametric space-time model from a Bayesian perspective. Nonlinear time dependence of covariates and the interactions among the covariates are constructed by local linear and piecewise linear models, allowing for more flexible orientation and position of the covariate plane by using time-varying basis functions. Space-varying covariate linkage coefficients are also incorporated to allow for the variation of space structures across the geographical location. The formulation accommodates uncertainty in the number and locations of the piecewise basis functions to characterize the global effects, spatially structured and unstructured random effects in relation to covariates. The proposed approach relies on variable selection-type mixture priors for uncertainty in the number and locations of basis functions and in the space-varying linkage coefficients. A simulation example is presented to evaluate the performance of the proposed approach with the competing models. A real data example is used for illustration.

中文翻译：

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具有时空相关协变量的贝叶斯潜在结构模型

时空数据需要灵活的回归模型，该模型可以对响应对空间和时间相关协变量的依赖性进行建模。在本文中，我们从贝叶斯的角度描述了一个半参数时空模型。协变量的非线性时间相关性和协变量之间的相互作用由局部线性和分段线性模型构建，允许通过使用时变基函数更灵活地定位协变量平面。还结合了空间变化的协变量链接系数，以允许跨地理位置的空间结构的变化。该公式适应分段基函数的数量和位置的不确定性，以表征与协变量相关的全局效应、空间结构化和非结构化随机效应。所提出的方法依赖于变量选择类型的混合先验来确定基函数的数量和位置以及空间变化的连锁系数的不确定性。提供了一个仿真示例来评估所提出的方法与竞争模型的性能。使用真实数据示例进行说明。