Spatial Statistics最新文献

The spatial variation in population-level disease rates can be estimated from aggregated disease data relating to $N$ areal units using Bayesian hierarchical models. Spatial autocorrelation in these data is captured by random effects that are assigned a Conditional autoregressive (CAR) prior, which assumes that neighbouring areal units exhibit similar disease rates. This approach ignores boundaries in the disease rate surface, which are locations where neighbouring units exhibit a step-change in their rates. CAR type models have been extended to account for this localised spatial smoothness, but they are computationally prohibitive for big data sets. Therefore this paper proposes a novel computationally efficient approach for localised spatial smoothing, which is motivated by a new study of mental ill health across $N=\text{32,754}$ Lower Super Output Areas in England. The approach is based on a computationally efficient ridge regression framework, where the spatial trend in disease rates is modelled by a set of anisotropic spatial basis functions that can exhibit either smooth or step change transitions in values between neighbouring areal units. The efficacy of this approach is evidenced by simulation, before using it to identify the highest rate areas and the magnitude of the health inequalities in four measures of mental ill health, namely antidepressant usage, benefit claims, depression diagnoses and hospitalisations.

Spatial trend estimation under potential heterogeneity is an important problem to extract spatial characteristics and hazards such as criminal activity. By focusing on quantiles, which provide substantial information on distributions compared with commonly used summary statistics such as means, it is often useful to estimate not only the average trend but also the high (low) risk trend additionally. In this paper, we propose a Bayesian quantile trend filtering method to estimate the non-stationary trend of quantiles on graphs and apply it to crime data in Tokyo between 2013 and 2017. By modeling multiple observation cases, we can estimate the potential heterogeneity of spatial crime trends over multiple years in the application. To induce locally adaptive Bayesian inference on trends, we introduce general shrinkage priors for graph differences. Introducing so-called shadow priors with multivariate distribution for local scale parameters and mixture representation of the asymmetric Laplace distribution, we provide a simple Gibbs sampling algorithm to generate posterior samples. The numerical performance of the proposed method is demonstrated through simulation studies.

We address the problem of spatial prediction for Hilbert data, when their spatial domain of observation is a river network. The reticular nature of the domain requires to use geostatistical methods based on the concept of Stream Distance, which captures the spatial connectivity of the points in the river induced by the network branching. Within the framework of Object Oriented Spatial Statistics (O2S2), where the data are considered as points of an appropriate (functional) embedding space, we develop a class of functional moving average models based on the Stream Distance. Both the geometry of the data and that of the spatial domain are thus taken into account. A consistent definition of covariance structure is developed, and associated estimators are studied. Through the analysis of the summer water temperature profiles in the Middle Fork River (Idaho, USA), our methodology proved to be effective, both in terms of covariance structure characterization and forecasting performance.

We propose a Bayesian stochastic cellular automata modeling approach to model the spread of wildfires with uncertainty quantification. The model considers a dynamic neighborhood structure that allows neighbor states to inform transition probabilities in a multistate categorical model. Additional spatial information is captured by the use of a temporally evolving latent spatio-temporal dynamic process linked to the original spatial domain by spatial basis functions. The Bayesian construction allows for uncertainty quantification associated with each of the predicted fire states. The approach is applied to a heavily instrumented controlled burn.

Since the emergence of the novel COVID-19 virus pandemic in December 2019, numerous mathematical models were published to assess the transmission dynamics of the disease, predict its future course, and evaluate the impact of different control measures. The simplest models make the basic assumptions that individuals are perfectly and evenly mixed and have the same social structures. Such assumptions become problematic for large developing countries that aggregate heterogeneous COVID-19 outbreaks in local areas. Thus, this paper proposes a spatial SEIRDV model that includes spatial vaccination coverage, spatial vulnerability, and level of mobility, to take into account the spatial–temporal clustering pattern of COVID-19 cases. The conclusion of this study is that immunity, government interventions, infectiousness and virulence are the main drivers of the spread of COVID-19. These factors should be taken into consideration when scientists, public policy makers and other stakeholders in the health community analyse, create and project future disease prevention scenarios. Such a model has a place for disease outbreaks that may occur in future, allowing for the inclusion of vaccination rates in a spatial manner.

Spatial data are widely used in various scenarios of life and are highly valued, and their analysis and research have achieved remarkable results. Spatial data have spatial effects and do not satisfy the assumption of independence; thus, the traditional econometric analysis methods cannot be directly used in spatial models, and the spatial autocorrelation and spatial heterogeneity of spatial data make the research more complicated and difficult. Generalized moment estimation(GMM) is a powerful tool for statistical modeling and inference of spatial data. Considering the case where there is a set of correctly specified moment conditions and another set of possibly misspecified moment conditions for spatial data, this paper proposes a GMM shrinkage method to estimate the unknown parameters for spatial autoregressive model with spatial autoregressive disturbances. The proposed GMM estimators are shown to enjoy oracle properties; i.e., it selects the valid moment conditions consistently from the candidate set and includes them into estimation automatically. The resulting estimator is asymptotically as efficient as the GMM estimator based on all valid moment conditions. Monte Carlo studies show that the method works well in terms of valid moment selection and the finite sample properties of its estimators.

Poisson and Negative Binomial Regression Models are often used to describe the relationship between a count dependent variable and a set of independent variables. However, these models fail to analyze data with an excess of zeros, being Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models the most appropriate to fit this kind of data. To Incorporate the spatial dimension into the count data models, Geographically Weighted Poisson Regression (GWPR), Geographically Weighted Negative Binomial Regression (GWNBR) and Geographically Weighted Zero-Inflated Poisson Regression (GWZIPR) have been developed, but the zero-inflation part of the negative binomial distribution is undeveloped in order to incorporate the overdispersion and the excess of zeros, as was at the beginning of the COVID-19 pandemic, whereas some places were having an outbreak of cases and in others places, there were no cases yet. Therefore, we propose a Geographically Weighted Zero-Inflated Negative Binomial Regression (GWZINBR) model which can be considered a general case for count data, since locally it can become a GWZIPR, GWNBR or a GWPR model. We applied this model to simulated data and to the cases of COVID-19 in South Korea at the beginning of the pandemic in 2020 and the results showed a better understanding of the phenomenon compared to the GWNBR model.

Ignoring potential spatial autocorrelation in georeferenced data may cause biased estimators. Furthermore, existing studies assume insufficiently flexible structure of spatial lag model for some practical applications, which makes it difficult to portray the complex relationship between responses and covariates. Thus, we propose a novel garrotized kernel machine estimation method for the nonparametric spatial lag model and develop an eigenvector spatial filtering algorithm with sparse regression to filter spatial autocorrelation out of the residuals. The “one-group-at-a-time” cyclical coordinate descent algorithm is introduced for a solution path of tuning parameters. Our method can better describe the potential nonlinear relationship between responses and covariates, making it possible to model high-order interaction effects among covariates. Numerical results and the analysis of commodity residential house prices in large and medium-sized Chinese cities indicate that the proposed method achieves better prediction performance compared with competing ones. The result of real data analysis can provide guidance for the government to take targeted suppression measures of house prices for different areas.

The Matérn family of covariance functions is currently the most popularly used model in spatial statistics, geostatistics, and machine learning to specify the correlation between two geographical locations based on spatial distance. Compared to existing covariance functions, the Matérn family has more flexibility in data fitting because it allows the control of the field smoothness through a dedicated parameter. Moreover, it generalizes other popular covariance functions. However, fitting the smoothness parameter is computationally challenging since it complicates the optimization process. As a result, some practitioners set the smoothness parameter at an arbitrary value to reduce the optimization convergence time. In the literature, studies have used various parameterizations of the Matérn covariance function, assuming they are equivalent. This work aims at studying the effectiveness of different parameterizations under various settings. We demonstrate the feasibility of inferring all parameters simultaneously and quantifying their uncertainties on large-scale data using the ExaGeoStat parallel software. We also highlight the importance of the smoothness parameter by analyzing the Fisher information of the statistical parameters. We show that the various parameterizations have different properties and differ from several perspectives. In particular, we study the three most popular parameterizations in terms of parameter estimation accuracy, modeling accuracy and efficiency, prediction efficiency, uncertainty quantification, and asymptotic properties. We further demonstrate their differing performances under nugget effects and approximated covariance. Lastly, we give recommendations for parameterization selection based on our experimental results.