Spatial Statistics最新文献

Geostatistical regression models are widely used in environmental and geophysical sciences to characterize the mean and dependence structures for spatio-temporal data. Traditionally, these models account for covariates solely in the mean structure, neglecting their potential impact on the spatio-temporal covariance structure. This paper addresses a significant gap in the literature by proposing a novel covariate-dependent covariance model within the spatio-temporal random-effects model framework. Our approach integrates covariates into the covariance function through a Cholesky-type decomposition, ensuring compliance with the positive-definite condition. We employ maximum likelihood for parameter estimation, complemented by an efficient expectation conditional maximization algorithm. Simulation studies demonstrate the superior performance of our method compared to conventional techniques that ignore covariates in spatial covariances. We further apply our model to a PM_2.5 dataset from Taiwan, highlighting wind speed’s pivotal role in influencing the spatio-temporal covariance structure. Additionally, we incorporate wind speed and sunshine duration into the covariance function for analyzing Taiwan ozone data, revealing a more intricate relationship between covariance and these meteorological variables.

To mitigate the negative effects of emerging wildlife diseases in biodiversity and public health it is critical to accurately forecast pathogen dissemination while incorporating relevant spatio-temporal covariates. Forecasting spatio-temporal processes can often be improved by incorporating scientific knowledge about the dynamics of the process using physical models. Ecological diffusion equations are often used to model epidemiological processes of wildlife diseases where environmental factors play a role in disease spread. Physics-informed neural networks (PINNs) are deep learning algorithms that constrain neural network predictions based on physical laws and therefore are powerful forecasting models useful even in cases of limited and imperfect training data. In this paper, we develop a novel ecological modeling tool using PINNs, which fits a feedforward neural network and simultaneously performs parameter identification in a partial differential equation (PDE) with varying coefficients. We demonstrate the applicability of our model by comparing it with the commonly used Bayesian stochastic partial differential equation method and traditional machine learning approaches, showing that our proposed model exhibits superior prediction and forecasting performance when modeling chronic wasting disease in deer in Wisconsin. Furthermore, our model provides the opportunity to obtain scientific insights into spatio-temporal covariates affecting spread and growth of diseases. This work contributes to future machine learning and statistical methodology development by studying spatio-temporal processes enhanced by prior physical knowledge.

Nonstationary and non-Gaussian spatial data are common in various fields, including ecology (e.g., counts of animal species), epidemiology (e.g., disease incidence counts in susceptible regions), and environmental science (e.g., remotely-sensed satellite imagery). Due to modern data collection methods, the size of these datasets have grown considerably. Spatial generalized linear mixed models (SGLMMs) are a flexible class of models used to model nonstationary and non-Gaussian datasets. Despite their utility, SGLMMs can be computationally prohibitive for even moderately large datasets (e.g., 5000 to 100,000 observed locations). To circumvent this issue, past studies have embedded nested radial basis functions into the SGLMM. However, two crucial specifications (knot placement and bandwidth parameters), which directly affect model performance, are typically fixed prior to model-fitting. We propose a novel approach to model large nonstationary and non-Gaussian spatial datasets using adaptive radial basis functions. Our approach: (1) partitions the spatial domain into subregions; (2) employs reversible-jump Markov chain Monte Carlo (RJMCMC) to infer the number and location of the knots within each partition; and (3) models the latent spatial surface using partition-varying and adaptive basis functions. Through an extensive simulation study, we show that our approach provides more accurate predictions than competing methods while preserving computational efficiency. We demonstrate our approach on two environmental datasets - incidences of plant species and counts of bird species in the United States.

In spatial statistics, fast and accurate parameter estimation, coupled with a reliable means of uncertainty quantification, can be challenging when fitting a spatial process to real-world data because the likelihood function might be slow to evaluate or wholly intractable. In this work, we propose using convolutional neural networks to learn the likelihood function of a spatial process. Through a specifically designed classification task, our neural network implicitly learns the likelihood function, even in situations where the exact likelihood is not explicitly available. Once trained on the classification task, our neural network is calibrated using Platt scaling which improves the accuracy of the neural likelihood surfaces. To demonstrate our approach, we compare neural likelihood surfaces and the resulting maximum likelihood estimates and approximate confidence regions with the equivalent for exact or approximate likelihood for two different spatial processes—a Gaussian process and a Brown–Resnick process which have computationally intensive and intractable likelihoods, respectively. We conclude that our method provides fast and accurate parameter estimation with a reliable method of uncertainty quantification in situations where standard methods are either undesirably slow or inaccurate. The method is applicable to any spatial process on a grid from which fast simulations are available.

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.