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复杂区域上的非参数密度估计AI 解读

Abstract We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements. This ensures high computational efficiency and enables great flexibility.…

基于偏微分方程惩罚空间回归的血流速度场估计AI 解读

We propose an innovative method for the accurate estimation of surfaces and spatial fields when prior knowledge of the phenomenon under study is available. The prior knowledge included in the model derives from physics, physiology, or mechanics of the problem at hand, and is formalized in terms of a partial differential equation governing the phenomenon behavior, as well as conditions that the phenomenon has to satisfy at the boundary of the problem domain. The proposed…

空间样条回归模型AI 解读

Summary We describe a model for the analysis of data distributed over irregularly shaped spatial domains with complex boundaries, strong concavities and interior holes. Adopting an approach that is typical of functional data analysis, we propose a spatial spline regression model that is computationally efficient, allows for spatially distributed covariate information and can impose various conditions over the boundaries of the domain. Accurate surface estimation is achieved…