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贝叶斯时空变化边界识别AI 解读

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed continuously over time) at arbitrary space-time coordinates, scientific interest often turns to gleaning information regarding zones of rapid spatial-temporal change. We develop Bayesian modeling and inference for directional rates of change…

利用预测堆叠的贝叶斯地统计分析AI 解读

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit analytically tractable posterior distributions for regression coefficients of predictors and the realizations of the spatial process conditional upon process parameters. We subsequently combine such inference by stacking these models across the…

空间曲率过程的贝叶斯建模AI 解读

Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as wombling boundaries,…

高度多元空间数据的图结构高斯过程模型AI 解读

Summary For multivariate spatial Gaussian process models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence between the variables. This is undesirable, especially in highly multivariate settings, where popular cross-covariance functions, such as multivariate Matérn functions, suffer from a curse of dimensionality as the numbers of parameters and floating-point operations…

基于分区域网格化高斯过程的高可扩展贝叶斯地统计建模AI 解读

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the regions in the partition using a sparsity-inducing directed acyclic graph (DAG). We extend the model over the DAG to a well-defined spatial process, which we call the Meshed Gaussian Process (MGP). A major contribution is the development of a…

高斯空间过程模型中块金效应的可识别性与一致性AI 解读

Abstract Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or microscale variability, and is called the ‘nugget’. We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, that is the sample size…

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We…

大型多性状遗传试验的分层空间过程模型AI 解读

This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets of multiple traits of interest. Direct application of such multivariate models to large spatial datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. The situation is…

不依赖变量顺序的区域数据协同区域化模型及多疾病制图应用AI 解读

Summary With the ready availability of spatial databases and geographical information system software, statisticians are increasingly encountering multivariate modelling settings featuring associations of more than one type: spatial associations between data locations and associations between the variables within the locations. Although flexible modelling of multivariate point-referenced data has recently been addressed by using a linear model of co-regionalization, existing…

空间响应面的梯度及其在城市土地价值中的应用AI 解读

For point-referenced spatial data, we often create explanatory models that introduce regression structure with error consisting of a spatial term and a white noise term. Here we consider more flexible regression structures that allow spatially varying regression coefficients. The resulting mean becomes a spatial response surface that is a linear combination of the components of the spatially varying coefficient vector. Of possible interest in this setting would be gradients…

空间过程模型下的方向变化率AI 解读

Spatial process models are now widely used for inference in many areas of application. In such contexts interest is often in the rate of change of a spatial surface at a given location in a given direction. Examples include temperature or rainfall gradients in meteorology, pollution gradients for environmental data, and surface roughness assessment for digital elevation models. Because the spatial surface is viewed as a random realization, all such rates of change are random…