Spatial Statistics最新文献

Consider a spatial blind source separation model in which the observed multivariate spatial data are assumed to be a linear mixture of latent stationary spatially uncorrelated random fields. The objective is to recover an unknown mixing procedure as well as the latent random fields. Recently, spatial blind source separation methods that are based on the simultaneous diagonalization of two or more scatter matrices were proposed. In cases involving uncontaminated data, such methods can solve the blind source separation problem, however, in the presence of outlying observations, these methods perform poorly. We propose a robust blind source separation method that employs robust global and local covariance matrices based on generalized spatial signs in simultaneous diagonalization. Simulation studies are employed to illustrate the robustness and efficiency of the proposed methods in various scenarios.

We analyze data occurring in a regular two-dimensional grid for spatial dependence based on spatial ordinal patterns (SOPs). After having derived the asymptotic distribution of the SOP frequencies under the null hypothesis of spatial independence, we use the concept of the type of SOPs to define the statistics to test for spatial dependence. The proposed tests are not only implemented for real-valued random variables, but a solution for discrete-valued spatial processes in the plane is provided as well. The performances of the spatial-dependence tests are comprehensively analyzed by simulations, considering various data-generating processes. The results show that SOP-based dependence tests have good size properties and constitute an important and valuable complement to the spatial autocorrelation function. To be more specific, SOP-based tests can detect spatial dependence in non-linear processes, and they are robust with respect to outliers and zero inflation. To illustrate their application in practice, two real-world data examples from agricultural sciences are analyzed.

Multiple-point simulation is a commonly used method in modeling complex curvilinear structures. The method is based on the application of training images that are open to manipulation. The present study introduces a new data-driven multiple-point simulation method that derives multiple point statistics directly from sparse data using copulas and applies them in simulation of complex mineral deposits. This method is based on simplification of N-dimensional copulas by its underlying two-dimensional copulas and taking advantage of conditional independence assumption to integrate information from different sources. The method was compared to Filtersim, a conventional multiple-point geostatistical method, through two synthetic data sets. Reproduction of cumulative distribution function, variogram, N-point connectivity, and visual patterns were considered in comparison. The copula-based multiple-point simulation (CMPS) method was implemented using trivial parts (almost 4%) of the synthetic data to extract required statistics while Filtersim was performed by giving the target image (100% data) as training image. Despite overwhelming data use in Filtersim, the CMPS showed compatible results to it. Application to synthetic data indicated that the method is a promising tool in the simulation of deposits with sparse data. The CMPS were applied in the simulation of two mineral deposits: (1) a porphyry copper deposit and (2) a magmatic iron deposit.

As global warming progresses, it is increasingly important to monitor and analyse spatio-temporal patterns of heat waves and other extreme climate-related events that impact urban areas. In this work, we present a novel dynamic spatio-temporal model by combining a state space model (SSM) and a generalised hyperbolic distribution to flexibly describe a spatial–temporal profile of the tail behaviour, skewness and kurtosis of the local urban temperature distribution of the greater Tokyo metropolitan area. Such a model can be used to study local dynamics of temperature effects, specifically those that characterise extreme heat or cold. The focus of the application in this paper will be heat wave events in the greater Tokyo metropolitan area which is known to be prone to some of the most severe heat wave events that have one of the largest population exposures due to high density living in Tokyo city. The advantages the proposed model offers are as follows: it accommodates skewed and fat-tail distributions for temperature profiles; the model can be expressed as a location-scale linear Gaussian SSM which allows the development of an efficient Monte Carlo mixture Kalman Filter solution for the estimation. The proposed model is compared with the Gaussian SSM through application to maximum temperature data in the Tokyo metropolitan area between 1978–2016. The result suggests that the proposed model estimates the temperature distribution more accurately than the conventional linear Gaussian SSM and that the predictive variance of our method tends to be smaller than that obtained from the conventional spate time linear Gaussian SSM benchmark model.

Correlation-based hierarchical clustering methods for time series typically are based on a suitable dissimilarity matrix derived from pairwise measures of association. Here, this dissimilarity is modified in order to take into account the presence of spatial constraints. This modification exploits the geometric structure of the space of correlation matrices, i.e. their Riemannian manifold. Specifically, the temporal correlation matrix (based on van der Waerden coefficient) is aggregated to the spatial correlation matrix (obtained from a suitable Matérn correlation function) via a geodesic in the Riemannian manifold. Our approach is presented and discussed using simulated and real data, highlighting its main advantages and computational aspects.

In this paper, we further investigate the problem of selecting a set of design points for universal kriging, which is a widely used technique for spatial data analysis. Our goal is to select the design points in order to make simultaneous predictions of the random variable of interest at a finite number of unsampled locations with maximum precision. Specifically, we consider as response a correlated random field given by a linear model with an unknown parameter vector and a spatial error correlation structure. We propose a new design criterion that aims at simultaneously minimizing the variation of the prediction errors at various points. We also present various efficient techniques for incrementally building designs for that criterion scaling well for high dimensions. Thus the method is particularly suitable for big data applications in areas of spatial data analysis such as mining, hydrogeology, natural resource monitoring, and environmental sciences or equivalently for any computer simulation experiments. We have demonstrated the effectiveness of the proposed designs through two illustrative examples: one by simulation and another based on real data from Upper Austria.

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.