Spatial Statistics最新文献

Recent wildfires in Australia have led to considerable economic loss and property destruction, and there is increasing concern that climate change may exacerbate their intensity, duration, and frequency. Hazard quantification for extreme wildfires is an important component of wildfire management, as it facilitates efficient resource distribution, adverse effect mitigation, and recovery efforts. However, although extreme wildfires are typically the most impactful, both small and moderate fires can still be devastating to local communities and ecosystems. Therefore, it is imperative to develop robust statistical methods to reliably model the full distribution of wildfire spread. We do so for a novel dataset of Australian wildfires from 1999 to 2019, and analyse monthly spread over areas approximately corresponding to Statistical Areas Level 1 and 2 (SA1/SA2) regions. Given the complex nature of wildfire ignition and spread, we exploit recent advances in statistical deep learning and extreme value theory to construct a parametric regression model using graph convolutional neural networks and the extended generalised Pareto distribution, which allows us to model wildfire spread observed on an irregular spatial domain. We highlight the efficacy of our newly proposed model and perform a wildfire hazard assessment for Australia and population-dense communities, namely Tasmania, Sydney, Melbourne, and Perth.

Spatial autoregressive model is widely concerned in the economic field, whereas when the data is missing, variable selection and parameter estimation of the model is quite challenging. Based on this, we discuss the variable selection in spatial autoregressive model with missing data. Under the condition that errors are independent and identically distributed, we have developed a penalized quasi-maximum likelihood method to achieve variable selection and parameter estimation simultaneously in the presence of missing responses. The method’s theoretical properties, including consistency and asymptotical normality, are established under certain assumptions. Meanwhile, an improved expectation–maximization algorithm is provided for optimizing the penalized quasi-maximum likelihood function. Simulations are conducted to examine the proposed method and assess the finite-sample performance. Additionally, we present a practical example to illustrate the method’s application.

Georeferenced data often contain missing values, and such missing values can considerably affect spatial modeling. A spatial location model can also suffer from this issue when there are missing values in its geographic distribution of weights. Although general imputation approaches have been developed, one distinguishing fact here is that spatial imputation generally performs better for georeferenced data because it can reflect a fundamental property of those data, that is, spatial autocorrelation or spatial dependency. This paper explores how spatial imputation exploiting spatial autocorrelation can contribute to estimating missing values in a weights surface for location modeling and subsequently improve solutions for spatial optimization, specifically p-median problems using a spatially imputed weights surface. This paper examines two spatial imputation methods, ordinary co-kriging and Moran eigenvector spatial filtering. Their results are compared with conventional linear regression, essentially Expectation-Maximization algorithm results for independent observations of Gaussian random variable cases. Simulation experiments show that spatial imputation produces better results for georeferenced data than simply ignoring any missing values and non-spatial imputation, and appropriately imputed values can enhance spatial optimization solutions, regardless of the number of medians, p.

Spatial areal models encounter the well-known and challenging problem of spatial confounding. This issue makes it arduous to distinguish between the impacts of observed covariates and spatial random effects. Despite previous research and various proposed methods to tackle this problem, finding a definitive solution remains elusive. In this paper, we propose a simplified version of the spatial+ approach that involves dividing the covariate into two components. One component captures large-scale spatial dependence, while the other accounts for short-scale dependence. This approach eliminates the need to separately fit spatial models for the covariates. We apply this method to analyse two forms of crimes against women, namely rapes and dowry deaths, in Uttar Pradesh, India, exploring their relationship with socio-demographic covariates. To evaluate the performance of the new approach, we conduct extensive simulation studies under different spatial confounding scenarios. The results demonstrate that the proposed method provides reliable estimates of fixed effects and posterior correlations between different responses.

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.