Spatial Statistics最新文献

Conductivity is an important indicator of the health of aquatic ecosystems. We model large amounts of lake conductivity data collected as part of the United States Environmental Protection Agency’s National Lakes Assessment using spatial indexing, a flexible and efficient approach to fitting spatial statistical models to big data sets. Spatial indexing is capable of accommodating various spatial covariance structures as well as features like random effects, geometric anisotropy, partition factors, and non-Euclidean topologies. We use spatial indexing to compare lake conductivity models and show that calcium oxide rock content, crop production, human development, precipitation, and temperature are strongly related to lake conductivity. We use this model to predict lake conductivity at hundreds of thousands of lakes distributed throughout the contiguous United States. We find that lake conductivity models fit using spatial indexing are nearly identical to lake conductivity models fit using traditional methods but are nearly 50 times faster (sample size 3,311). Spatial indexing is readily available in the spmodel R package.

Geographically Weighted Principal Component Analysis (GWPCA) is an extension of classical PCA to deal with the spatial heterogeneity of geographical data. This heterogeneity results in a variance–covariance matrix that is not stationary but changes with the geographical location. Despite its usefulness, this method presents some unsolved issues, such as finding an appropriate bandwidth (size of the vicinity) as a function of the retained components. In this work, we address the problem of calculating principal components for geographical data from a new perspective that overcomes this problem. Specifically we propose a scale-location model which uses generalized additive models (GAMs) to calculate means for each variable and a correlation matrix that relates the variables, both depending on the spatial location. It should be noticed that although we deal with geographic data, our methodology cannot be considered strictly spatial since we assume that there is not a spatial correlation structure in the error term.

Our approach does not require to calculate an optimal bandwidth as a function of the number of components retained in the analysis. Instead, the covariance matrix is estimated using smooth functions adapted to the data, so the smoothness can be different for each element of the matrix. The proposed methodology was tested with simulated data and compared with GWPCA. The result was a better representation of the data structure in the proposed method. Finally, we show the possibilities of our method in a problem with real data regarding air pollution and socioeconomic factors.

The spatial analysis of traffic accidents has long been a useful tool for authorities to implement effective preventive measures. Initial studies were conducted at the areal level considering administrative or traffic-related units, but a more precise analysis at the street level is necessary for developing targeted interventions. In recent years, there has been a significant increase in studies conducted at the road network level, which require using new statistical techniques that are suitable for linear networks. However, modeling accident counts at the street level presents several challenges, primarily due to the need for accurate georeferenced data to correctly assign events to specific streets or road segments. Despite advancements in geocoding methods, discrepancies can still arise between the true event locations and the locations mapped by a geocoding method. In this paper, we propose a model to deal with the presence of location uncertainty and enable an analysis of accident intensity constrained to the road network. The model does not assume any specific mechanism for location uncertainty, as this reflects the most common practical scenario. By tackling this inherent problem, the proposed model aims to enhance the accuracy of accident analysis and contribute to the development of effective preventive measures for traffic safety. The model is evaluated with both a simulation study and a case study on the city of Valencia, Spain. For the latter, the proposed model reveals a greater association of road intersections with accident rates than that estimated by the standard model.

This paper explores the estimators of parameters for a spatial data single-index model which has measurement errors of covariates in the nonparametric part. The related estimations are considered to combine a local-linear smoother based simulation-extrapolation (SIMEX) algorithm, the estimation equation and the estimation method for profile maximum likelihood. Under regular conditions, asymptotic properties of the link function and uncertain estimators are derived. As verified in simulations, the performance of the estimators is satisfactory. Finally, an application to a real dataset is illustrated.

The inclusion of the geographic information into regression models is becoming increasingly popular due to the increased availability of corresponding geo-referenced data. In this paper, a novel framework for combining spatio-temporal regression techniques and artificial neural network (ANN) regression models is presented. The key idea is to use the universal approximation property of the ANN function to account for an arbitrary spatial pattern in the dependent variable by including geographic coordinate variables as regressors. Moreover, the implicit location-specific effects are allowed to exhibit arbitrary interaction effects with other regressors such as a time variable. In contrast to other machine learning approaches for spatio-temporal data, the likelihood framework of the classic (linear) spatio-temporal regression model is preserved. This allows, inter alia, for inference regarding marginal effects and associated confidence. The framework also allows for non-normal conditional distributions, conditional spatial correlation, arbitrary trend and seasonality. These features are demonstrated in a simulation section and two data examples, using linear spatio-temporal models as a reference.

Consider a spatial blind source separation model in which the observed multivariate spatial data are assumed to be a linear mixture of latent stationary spatially uncorrelated random fields. The objective is to recover an unknown mixing procedure as well as the latent random fields. Recently, spatial blind source separation methods that are based on the simultaneous diagonalization of two or more scatter matrices were proposed. In cases involving uncontaminated data, such methods can solve the blind source separation problem, however, in the presence of outlying observations, these methods perform poorly. We propose a robust blind source separation method that employs robust global and local covariance matrices based on generalized spatial signs in simultaneous diagonalization. Simulation studies are employed to illustrate the robustness and efficiency of the proposed methods in various scenarios.

We analyze data occurring in a regular two-dimensional grid for spatial dependence based on spatial ordinal patterns (SOPs). After having derived the asymptotic distribution of the SOP frequencies under the null hypothesis of spatial independence, we use the concept of the type of SOPs to define the statistics to test for spatial dependence. The proposed tests are not only implemented for real-valued random variables, but a solution for discrete-valued spatial processes in the plane is provided as well. The performances of the spatial-dependence tests are comprehensively analyzed by simulations, considering various data-generating processes. The results show that SOP-based dependence tests have good size properties and constitute an important and valuable complement to the spatial autocorrelation function. To be more specific, SOP-based tests can detect spatial dependence in non-linear processes, and they are robust with respect to outliers and zero inflation. To illustrate their application in practice, two real-world data examples from agricultural sciences are analyzed.

Multiple-point simulation is a commonly used method in modeling complex curvilinear structures. The method is based on the application of training images that are open to manipulation. The present study introduces a new data-driven multiple-point simulation method that derives multiple point statistics directly from sparse data using copulas and applies them in simulation of complex mineral deposits. This method is based on simplification of N-dimensional copulas by its underlying two-dimensional copulas and taking advantage of conditional independence assumption to integrate information from different sources. The method was compared to Filtersim, a conventional multiple-point geostatistical method, through two synthetic data sets. Reproduction of cumulative distribution function, variogram, N-point connectivity, and visual patterns were considered in comparison. The copula-based multiple-point simulation (CMPS) method was implemented using trivial parts (almost 4%) of the synthetic data to extract required statistics while Filtersim was performed by giving the target image (100% data) as training image. Despite overwhelming data use in Filtersim, the CMPS showed compatible results to it. Application to synthetic data indicated that the method is a promising tool in the simulation of deposits with sparse data. The CMPS were applied in the simulation of two mineral deposits: (1) a porphyry copper deposit and (2) a magmatic iron deposit.

As global warming progresses, it is increasingly important to monitor and analyse spatio-temporal patterns of heat waves and other extreme climate-related events that impact urban areas. In this work, we present a novel dynamic spatio-temporal model by combining a state space model (SSM) and a generalised hyperbolic distribution to flexibly describe a spatial–temporal profile of the tail behaviour, skewness and kurtosis of the local urban temperature distribution of the greater Tokyo metropolitan area. Such a model can be used to study local dynamics of temperature effects, specifically those that characterise extreme heat or cold. The focus of the application in this paper will be heat wave events in the greater Tokyo metropolitan area which is known to be prone to some of the most severe heat wave events that have one of the largest population exposures due to high density living in Tokyo city. The advantages the proposed model offers are as follows: it accommodates skewed and fat-tail distributions for temperature profiles; the model can be expressed as a location-scale linear Gaussian SSM which allows the development of an efficient Monte Carlo mixture Kalman Filter solution for the estimation. The proposed model is compared with the Gaussian SSM through application to maximum temperature data in the Tokyo metropolitan area between 1978–2016. The result suggests that the proposed model estimates the temperature distribution more accurately than the conventional linear Gaussian SSM and that the predictive variance of our method tends to be smaller than that obtained from the conventional spate time linear Gaussian SSM benchmark model.