Spatial Statistics最新文献

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.

Binary spatio-temporal data are common in many application areas. Such data can be considered from many perspectives, including via deterministic or stochastic cellular automata (CA), where local rules govern the transition probabilities that describe the evolution of the 0 and 1 states across space and time. One implementation of a stochastic CA for such data is via a spatio-temporal generalized linear model (or mixed model), with the local rule covariates being included in the transformed mean response. However, in many applications we do have a complete understanding of the local rules and must instead explore the rules space, which can be accomplished through symbolic regression. Even with a learned rule space, the data-driven rules may be insufficient to describe the process behavior and it is helpful to augment the transformed linear predictor with a latent spatio-temporal dynamic process. Here, we demonstrate for the first time that an echo state network (ESN) latent process can be used to enhance symbolic regression-learned local rule covariates. We implement this in a hierarchical Bayesian framework with regularized horseshoe priors on the ESN output weight matrices, which extends the ESN literature as well. Finally, we gain added expressiveness from the ESNs by considering an ensemble of ESN reservoirs, which we accommodate through weighted model averaging, which is also new to the ESN literature. We demonstrate our methodology on a simulated process in which we assume we do not know all of the local CA rules, as well as on multiple environmental data sets.

This article studies the use of asymmetric loss functions for the optimal prediction of positive-valued spatial processes. We focus on the family of power-divergence loss functions with properties such as continuity, convexity, connections to well known divergence measures, and the ability to control the asymmetry and behaviour of the loss function via a power parameter. The properties of power-divergence loss functions, optimal power-divergence (OPD) spatial predictors, and related measures of uncertainty quantification are studied. In addition, we examine in general the notion of asymmetry in loss functions defined for positive-valued spatial processes and define an asymmetry measure, which we apply to the family of power-divergence loss functions and other common loss functions. The paper concludes with a simulation study comparing the optimal power-divergence predictor to predictors derived from other common loss functions. Finally, we illustrate OPD spatial prediction on a dataset of zinc measurements in the soil of a floodplain of the Meuse River, Netherlands.

Several deep learning methods for spatial data have been developed that report good performance in a big data setting. These methods typically require the choice of an appropriate kernel and some tuning of hyperparameters, which are contributing reasons for poor performance on smaller data sets.

In this paper, we propose a mathematical construction of a graph-based neural network for spatial prediction that substantially generalizes the KCN model in [Appleby, Liu and Liu (2020). Kriging convolutional networks. In Proc. AAAI Conf. AI 34, pp. 3187–3194]. In particular, our model, referred to as SPONGE, allows for integrated learning of the convolutional kernel, admits higher order neighborhood structures and can make use of the distance between locations in the neighborhood and between labels of neighboring nodes. All of this yields higher flexibility in capturing spatial correlations.

We investigate in simulation studies including small, medium and (reasonably) large data sets in what situations and to what extent SPONGE comes close to or (if the conditions for optimality are violated) even beats universal Kriging, whose predictions incur a high computational cost if $n$ is large. Furthermore we study the improvement for general SPONGE in comparison with the usual KCN.

Finally, we compare various graph-based neural network models on larger real world data sets and apply our method to the prediction of soil organic carbon in the southern part of Malawi.

Profile likelihoods are rarely used in geostatistical models due to the computational burden imposed by repeated decompositions of large variance matrices. Accounting for uncertainty in covariance parameters can be highly consequential in geostatistical models as some covariance parameters are poorly identified, the problem is severe enough that the differentiability parameter of the Matern correlation function is typically treated as fixed. The problem is compounded with anisotropic spatial models as there are two additional parameters to consider. In this paper, we make the following contributions: Firstly, a methodology is created for profile likelihoods for Gaussian spatial models with Matérn family of correlation functions, including anisotropic models. This methodology adopts a novel reparameterization for generation of representative points, and uses GPUs for parallel profile likelihoods computation in software implementation. Then, we show the profile likelihood of the Matérn shape parameter is often quite flat but still identifiable, it can usually rule out very small values. Finally, simulation studies and applications on real data examples show that profile-based confidence intervals of covariance parameters and regression parameters have superior coverage to the traditional standard Wald type confidence intervals.

Statistical models for spatial processes play a central role in analyses of spatial data. Yet, it is the simple, interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest. Here, we propose a new, flexible class of spatial-process models, which we refer to as spatial Bayesian neural networks (SBNNs). An SBNN leverages the representational capacity of a Bayesian neural network; it is tailored to a spatial setting by incorporating a spatial “embedding layer” into the network and, possibly, spatially-varying network parameters. An SBNN is calibrated by matching its finite-dimensional distribution at locations on a fine gridding of space to that of a target process of interest. That process could be easy to simulate from or we may have many realisations from it. We propose several variants of SBNNs, most of which are able to match the finite-dimensional distribution of the target process at the selected grid better than conventional BNNs of similar complexity. We also show that an SBNN can be used to represent a variety of spatial processes often used in practice, such as Gaussian processes, lognormal processes, and max-stable processes. We briefly discuss the tools that could be used to make inference with SBNNs, and we conclude with a discussion of their advantages and limitations.

Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This study proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The model is based on Bernstein polynomial (BP) basis functions and utilizes a Bayesian approach for estimating unknown quantities and parameters. The paper explores the advantages and limitations of the BP model in capturing complex shapes and patterns while ensuring numerical stability. The main contributions of this work include the development of an innovative model designed for SFD using BP, the presence of a random effect to address associations between irregularly spaced observations, and a comprehensive simulation study to evaluate models’ performance under various scenarios. The work also presents one real application of Temperature in Mexico City, showcasing practical illustrations of the proposed model.