Spatial Statistics最新文献

The vast growth of spatial datasets in recent decades has fueled the development of many statistical methods for detecting spatial patterns. Two of the most commonly studied spatial patterns are clustering, loosely defined as datapoints with similar attributes existing close together, and dispersion, loosely defined as the semi-regular placement of datapoints with similar attributes. In this work, we develop a hypothesis test to detect spatial clustering or dispersion at specific distances in categorical areal data. Such data consists of a set of spatial regions whose boundaries are fixed and known (e.g., counties) associated with a categorical random variable (e.g. whether the county is rural, micropolitan, or metropolitan). We propose a method to extend the positive area proportion function (developed for detecting spatial clustering in binary areal data) to the categorical case. This proposal, referred to as the categorical positive areal proportion function test, can detect various spatial patterns, including homogeneous clusters, heterogeneous clusters, and dispersion. Our approach is the first method capable of distinguishing between different types of clustering in categorical areal data. After validating our method using an extensive simulation study, we use the categorical positive area proportion function test to detect spatial patterns in Boulder County, Colorado USA biological, agricultural, built and open conservation easements.

We propose novel second/higher-order summary statistics for inhomogeneous spatio-temporal point processes when the spatial locations are limited to a linear network. More specifically, letting the spatial distance between events be measured by a regular distance metric, appropriate forms of $K$- and $J$-functions are introduced, and their theoretical relationships are studied. The theoretical forms of our proposed summary statistics are investigated under homogeneity, Poissonness, and independent thinning. Moreover, non-parametric estimators are derived, facilitating the use of our proposed summary statistics to study the spatio-temporal dependence between events. Through simulation studies, we demonstrate that our proposed $J$-function effectively identifies spatio-temporal clustering, inhibition, and randomness. Finally, we examine spatio-temporal dependencies for street crimes in Valencia, Spain, and traffic accidents in New York, USA.

The outliers in the data set have a potential influence on the statistical inference and can provide some useful information behind the data set, the methodology for outlier detection and accommodation is always an important topic in data analysis. For spatial data, its influence not only affects coefficient estimation but model selection. The traditional method usually carries out outlier detection, model selection and variable selection step by step, so the data processing efficiency is not high. In order to further improve the efficiency and accuracy of data processing, based on the general spatial model, we consider a technique to achieve outlier detection, along with model and variable estimation in one step. In the general spatial model, we add a mean shift parameter for each data point to identify outliers. Penalized likelihood estimation (PLE) is proposed to simultaneously detect outliers, and to select spatial models and explanatory variables for spatial data. This method correctly identifies multiple outliers, provides a proper spatial model, and corrects coefficient estimation without removing outliers in numerical simulation and case analysis. Compared to current methods, PLE detects outliers more quickly, and solves the optimization problem to select spatial models and explanatory variables. Calculation is easy using the optimized solnp function in R software.

Transfer learning is generally regarded as a beneficial technique for utilizing external information to enhance learning performance on target tasks. However, current research on transfer learning in high-dimensional regression models does not take into account both the location information of the data and the explicit utilization of prior knowledge. In the framework of transfer learning, this study seeks to resolve the spatial autoregressive problem and investigate the impact of introducing linear constraints. In this paper, a two-step transfer learning approach and a transferable source detection algorithm based on cross-validation are proposed when the input dimensions of the source and target datasets are the same. When the input dimensions are different, this paper suggests a straightforward and workable incremental transfer learning method. Additionally, for the estimating model developed under this method, Karush–Kuhn–Tucker (KKT) conditions and degrees of freedom are determined, and a Bayesian Information Criterion (BIC) is created for choosing hyperparameters. The effectiveness of the proposed methods is proven by numerical calculations, and the performance of the model in transfer learning estimation is improved by the addition of linear constraints.

Particulate matter (PM) has emerged as a primary air quality concern due to its substantial impact on human health. Many recent research works suggest that PM_2.5 concentrations depend on meteorological conditions. Enhancing current pollution control strategies necessitates a more holistic comprehension of PM_2.5 dynamics and the precise quantification of spatiotemporal heterogeneity in the relationship between meteorological factors and PM_2.5 levels. The spatiotemporal varying coefficient model stands as a prominent spatial regression technique adept at addressing this heterogeneity. Amidst the challenges posed by the substantial scale of modern spatiotemporal datasets, we propose a pioneering distributed estimation method (DEM) founded on multivariate spline smoothing across a domain’s triangulation. This DEM algorithm ensures an easily implementable, highly scalable, and communication-efficient strategy, demonstrating almost linear speedup potential. We validate the effectiveness of our proposed DEM through extensive simulation studies, demonstrating that it achieves coefficient estimations akin to those of global estimators derived from complete datasets. Applying the proposed model and method to the US daily PM_2.5 and meteorological data, we investigate the influence of meteorological variables on PM_2.5 concentrations, revealing both spatial and seasonal variations in this relationship.

In this work, we consider space–time point processes and study their continuous space–time evolution. We propose an innovative nonparametric methodology to estimate the unknown space–time density of the point pattern, or, equivalently, to estimate the intensity of an inhomogeneous space–time Poisson point process. The presented approach combines maximum likelihood estimation with roughness penalties, based on differential operators, defined over the spatial and temporal domains of interest. We first establish some important theoretical properties of the considered estimator, including its consistency. We then develop an efficient and flexible estimation procedure that leverages advanced numerical and computation techniques. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can effectively capture complex multi-modal and strongly anisotropic spatio-temporal point patterns; moreover, these point patterns may be observed over planar or curved domains with non-trivial geometries, due to geographic constraints, such as coastal regions with complicated shorelines, or curved regions with complex orography. In addition to providing estimates, the method’s functionalities also include the introduction of appropriate uncertainty quantification tools. We thoroughly validate the proposed method, by means of simulation studies and applications to real-world data. The obtained results highlight significant advantages over state-of-the-art competing approaches.

In order to prevent and/or forecast road accidents, the statistical modeling of spatial dependence and potential risk factors is a major asset. The main goal of this article is to predict the number of accidents on a certain area by considering georeferenced accident locations crossed with variables characterizing the studied geographical area such as road characteristics as well as sociodemographic and global infrastructure variables. We model the accident point pattern by a spatial log-Gaussian Cox process (LGCP). To reduce the computation burden of LGCP models in this high-dimensional setting, we suggest a two-step procedure: to perform first automatic variable selection methods based on Poisson regression, Poisson aggregation and random forest and in a second step, to use the selected variables and perform LGCP model analysis. The dataset consists in road accidents occurred between 2017 and 2019 in the CAGB (urban community of Besançon), France. Based on LGCP analysis, we are able to identify the principal risk factors of road accidents and risky areas from CAGB region.

We present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov random field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable order, depending on the neighbors’ values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependence neighborhood structure as a graph in a tree format, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility.

Selecting correct specification in spatial model frameworks is a relevant research topic in spatial econometrics. The purpose of this paper is to examine and contrast two well-known model selection strategies, Specific-to-General, Stge, and General-to-Specific, Gets, in the context of spatial probit models. The results obtained from these classical methods are juxtaposed with those generated through the utilization of a powerful machine learning algorithm: Gradient Boosting. The paper includes an extensive Monte Carlo experiment to compare the performance of these three strategies with small and medium sample sizes. The results show that under ideal conditions, both classical strategies obtain similar results for medium-sized samples, but for small samples, Stge performs slightly better than Gets. The Gradient Boosting algorithm obtains slightly higher success rates than the classical strategies, especially with small samples sizes. Finally, the flow of both strategies is illustrated using a well-known dataset on the probability of businesses reopening in New Orleans in the aftermath of Hurricane Katrina.