Spatial Statistics最新文献

The proliferation of mobile devices has led to the collection of large amounts of population data. This situation has prompted the need to utilize this rich, multidimensional data in practical applications. In response to this trend, we have integrated functional data analysis (FDA) and factor analysis to address the challenge of predicting hourly population changes across various districts in Tokyo. Specifically, by assuming a Gaussian process, we avoided the large covariance matrix parameters of the multivariate normal distribution. In addition, the data were both time and spatially dependent between districts. To capture various characteristics, a Bayesian factor model was introduced, which modeled the time series of a small number of common factors and expressed the spatial structure through factor loading matrices. Furthermore, the factor loading matrices were made identifiable and sparse to ensure the interpretability of the model. We also proposed a Bayesian shrinkage method as a systematic approach for factor selection. Through numerical experiments and data analysis, we investigated the predictive accuracy and interpretability of our proposed method. We concluded that the flexibility of the method allows for the incorporation of additional time series features, thereby improving its accuracy.

Measuring bivariate spatial association plays a key role in understanding the spatial relationships between two types of geographical flow (hereafter referred to as “flow”). However, existing studies usually use multiple scales to analyze bivariate associations of flows, leading to the results at larger scales can be strongly affected by the results at smaller scales. Moreover, the planar space assumption of most existing studies is unsuitable for network-constrained flows. To solve these problems, a network incremental flow cross K-function (NIFK) is developed in this study by extending the cross K-function for points into a flow context. Specifically, two versions of NIFK were developed in this study: the global version to check whether bivariate associations exist in the whole study area and the local version to identify specific locations where associations occur. Experiments on three simulated datasets demonstrate the advantages of the proposed method over an available alternative method. A case study conducted using Xiamen taxi and ride-hailing service datasets demonstrates the usefulness of the proposed method. The detected bivariate spatial association provides deep insights for understanding the competition between taxi services and ride-hailing services.

A scientific grasp of the macro law of coal mining accidents can contribute to strengthening their prevention and control and guaranteeing a stable energy supply. In this study, 2,269 investigation reports of China's coal mining accidents from 2005 to 2022 were adopted as the basic data source, and GIS spatial analysis and rescaled range analysis methods were utilized to comprehensively reveal the spatial-temporal distribution features, and evolutionary patterns of coal mining accidents in China. The findings indicate that the numbers of gas explosion, permeability, outburst, suffocation and roof fall accidents has rapidly declined. The coverage area of coal mining accidents has gradually moved toward western of China. However, the center of the area covered by coal mining accidents during the study period was mainly concentrated in Shanxi and Henan Provinces. Besides, the number of deaths resulting from coal mining accidents across the country has gradually decreased, while the time series exhibited high continuity, with future changes consistent with past changes. The average cycle period of the coal mining accident sequence was 5 years. Through the systematic analysis of coal mine accidents conducted in this research, the law of accident occurrence was more comprehensively revealed, providing a reference and basis for the government and enterprises to implement precise preventive measures.

In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest. Large space–time datasets call for new numerical methods to efficiently process them. The Stochastic Partial Differential Equation (SPDE) approach has proven to be effective for the estimation and the prediction in a spatial context. We present here the advection–diffusion SPDE with first–order derivative in time which defines a large class of nonseparable spatio-temporal models. A Gaussian Markov random field approximation of the solution to the SPDE is built by discretizing the temporal derivative with a finite difference method (implicit Euler) and by solving the spatial SPDE with a finite element method (continuous Galerkin) at each time step. The “Streamline Diffusion” stabilization technique is introduced when the advection term dominates the diffusion. Computationally efficient methods are proposed to estimate the parameters of the SPDE and to predict the spatio-temporal field by kriging, as well as to perform conditional simulations. The approach is applied to a solar radiation dataset. Its advantages and limitations are discussed.

By allowing covariate-specific bandwidths for estimating spatially varying coefficients, the multiscale geographically weighted regression (MGWR) model can simultaneously explore spatial non-stationarity and multiple operational scales of the corresponding geographical processes. Treating the constant coefficients as an extreme situation which corresponds to the global scale and infinite covariate bandwidth, the traditional linear regression, GWR and mixed GWR models are special cases of the MGWR model. An appropriately-specified GWR-based model would be beneficial to the understanding of the general underlying processes, especially for their operational scales. To specify an appropriate model, the key issue is to determine how many MGWR coefficient(s) should be constant. Along the traditional statistical line of thought, we propose a residual-based bootstrap method to test spatial non-stationarity of the MGWR coefficients, which can underpin our understanding of the characteristics of regression relationships in statistics. The simulation experiment validates the proposed test, and demonstrates that it is of valid Type I error and satisfactory power, and is robust to different types of model error distributions. The applicability of the proposed test is demonstrated in a real-world case study on the Shanghai housing prices.

‘Outdegree’ from directed graph theory is used to measure the salience of individual locations in the transmission of Covid-19 morbidity through the spatiotemporal network of contagion and their salience in the spatiotemporal diffusion of vaccination rollout. A spatial econometric model in which morbidity varies inversely with vaccination rollout, and vaccination rollout varies directly with morbidity is used to calculate dynamic auto-outdegrees for morbidity and dynamic cross-outdegrees for the effect of vaccination on morbidity. The former identifies hot spots of contagion, and the latter identifies locations in which vaccination rollout is particularly effective in reducing national morbidity. These outdegrees are calculated analytically rather than simulated numerically.

Standard techniques such as leave-one-out cross-validation (LOOCV) might not be suitable for evaluating the predictive performance of models incorporating structured random effects. In such cases, the correlation between the training and test sets could have a notable impact on the model’s prediction error. To overcome this issue, an automatic group construction procedure for leave-group-out cross validation (LGOCV) has recently emerged as a valuable tool for enhancing predictive performance measurement in structured models. The purpose of this paper is (i) to compare LOOCV and LGOCV within structured models, emphasizing model selection and predictive performance, and (ii) to provide real data applications in spatial statistics using complex structured models fitted with INLA, showcasing the utility of the automatic LGOCV method. First, we briefly review the key aspects of the recently proposed LGOCV method for automatic group construction in latent Gaussian models. We also demonstrate the effectiveness of this method for selecting the model with the highest predictive performance by simulating extrapolation tasks in both temporal and spatial data analyses. Finally, we provide insights into the effectiveness of the LGOCV method in modeling complex structured data, encompassing spatio-temporal multivariate count data, spatial compositional data, and spatio-temporal geospatial data.

The connection between Gaussian random fields and Markov random fields has been well-established in Euclidean spaces, with Matérn covariance functions playing a pivotal role. In this paper, we explore the extension of this link to circular spaces and uncover different results. It is known that Matérn covariance functions are not always positive definite on the circle; however, the circular Matérn covariance functions are shown to be valid on the circle and are the focus of this paper. For these circular Matérn random fields on the circle, we show that the corresponding Markov random fields can be obtained explicitly on equidistance grids. Consequently, the equivalence between the circular Matérn random fields and Markov random fields is then exact and this marks a departure from the Euclidean space counterpart, where only approximations are achieved. Moreover, the key motivation in Euclidean spaces for establishing such link relies on the assumption that the corresponding Markov random field is sparse. We show that such sparsity does not hold in general on the circle. In addition, for the sparse Markov random field on the circle, we derive its corresponding Gaussian random field.

Natural sciences such as geology and forestry often utilize regression models for spatial data with many predictors and small to moderate sample sizes. In these settings, efficient estimation of the regression parameters is crucial for both model interpretation and prediction. We propose a dimension reduction approach for spatial regression that assumes certain linear combinations of the predictors are immaterial to the regression. The model and corresponding inference provide efficient estimation of regression parameters while accounting for spatial correlation in the data. We employed the maximum likelihood estimation approach to estimate the parameters of the model. The effectiveness of the proposed model is illustrated through simulation studies and the analysis of a geochemical data set, predicting rare earth element concentrations within an oil and gas reserve in Wyoming. Simulation results indicate that our proposed model offers a significant reduction in the mean square errors and variation of the regression coefficients. Furthermore, the method provided a 50% reduction in prediction variance for rare earth element concentrations within our data analysis.

In this study, we introduce the integrated deviance information criterion (DIC) for nested and non-nested model selection problems in heteroskedastic spatial autoregressive models. In a Bayesian estimation setting, we assume that the idiosyncratic error terms of our spatial autoregressive model have a scale mixture of normal distributions, where the scale mixture variables are latent variables that induce heteroskedasticity. We first derive the integrated likelihood function by analytically integrating out the scale mixture variables from the complete-data likelihood function. We then use the integrated likelihood function to formulate the integrated DIC measure. We investigate the finite sample performance of the integrated DIC in selecting the true model in a simulation study. The simulation results show that the integrated DIC performs satisfactorily and can be useful for selecting the correct model in specification search exercises. Finally, in a spatially augmented economic growth model, we use the integrated DIC to choose the spatial weights matrix that leads to better predictive accuracy.