Several model comparison techniques exist to select the best fitting model from a set of candidate models. This study explores the performance of model comparison tools that are commonly used in Bayesian spatial disease mapping and that are available among several Bayesian software packages: the deviance information criterion (DIC), the Watanabe–Akaike information criterion (WAIC) and the log marginal

The economic literature has largely ignored the existence of global common factors and local spatial dependence in the assessment of the real effects of U.S. banking deregulation. Motivated by consistency concerns, this study uses spatial econometric models with common factors to analyze the impact of U.S. banking deregulation on county-level economic growth during the 1970–2000 period. We estimate

The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are applied to preferentially sampled data without adjustment. Detecting preferential sampling is currently a technically demanding task. As a result, the problem is

Modelling the small-area spatio-temporal dynamics of the Covid-19 pandemic is of major public health importance, because it allows health agencies to better understand how and why the virus spreads. However, in Scotland during the first wave of the pandemic testing capacity was severely limited, meaning that large numbers of infected people were not formally diagnosed as having the virus. As a result

This paper presents a new algorithm for statistical inference and analysis of spatial patterns assumed to be realisations of Gibbs point processes. This approach has a general character and it contributes to the existing methods based on Approximate Bayesian Computation, by providing control properties of the proposed solution. Results on simulated data and real data are presented. The real data application

The problem of estimating the spatio-functional quantile regression for a given spatial mixing structure (Xi,Yi)∈F×R, when i∈ZN, N≥1 and F is a separable Hilbert space, is investigated. We construct and compare four estimators of the regression quantile. The proposed estimators cover the two main aspects of the statistical analysis, namely the parametric and nonparametric approaches. Precisely, using

Detailed spatial representation of socioeconomic data has the potential to improve the reliability and quality of spatial assessment. In this paper, we propose a novel method to spatialize the transportation industry output of Hunan Province in China by disaggregating the administrative-unit level to the grid-cell one based on the classification and regression tree and the spatial copula model. The

This paper presents a case study carried out in multiple cities of the Valencian Community (Spain) to determine the effect of sociodemographic and road characteristics on traffic accident risk. The analyzes are performed at the road segment level, considering the linear network representing the road structure of each city as a spatial lattice. The number of accidents observed in each road segment from

We propose a model based on discrete latent variables, which are spatially associated and time specific, for the analysis of incident cases of SARS-CoV-2 infections. We assume that for each area the sequence of latent variables across time follows a Markov chain with initial and transition probabilities that also depend on latent variables in neighboring areas. The model is estimated by a Markov chain

We address the problem of characterizing spatially variable Natural Background Levels (NBLs) of concentrations of chemical species of environmental concern in a large-scale groundwater body. Assessment of NBLs is critical to identify significant trends of (possibly hazardous) chemical concentrations in aquifer systems, the latter being typically associated with spatially heterogeneous hydrogeochemical

The statistical modeling of multivariate count data observed on a space–time lattice has generally focused on using a hierarchical modeling approach where space–time correlation structure is placed on a continuous, latent, process. The count distribution is then assumed to be conditionally independent given the latent process. However, in many real-world applications, especially in the modeling of

Spatial direction vector data can be represented cylindrically by linear magnitudes and circular angles. We analyze such data by using a hierarchical Markov random field model with latent discrete classes and conditionally independent cylindrical data given the classes. The structure of a Potts model segments the spatial domain, and each class defines a cylindrical density that represents a specific

Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM) model. MFM approach leads to a consistent and simultaneous estimate of the intensity surface of spatial point pattern and the clustering information (number of clusters

Several methods have been proposed in the spatial statistics literature to analyse big data sets in continuous domains. However, new methods for analysing high-dimensional areal data are still scarce. Here, we propose a scalable Bayesian modelling approach for smoothing mortality (or incidence) risks in high-dimensional data, that is, when the number of small areas is very large. The method is implemented

Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to construct generalizations of classical Gibbs models. In this paper, we extend the Geyer saturation point process model to the spatio-temporal multi-scale framework.

Modeling the spatial correlation structure of coregionalized data is a frequent task in numerous fields of the natural sciences. Even in the isotropic case, experimental covariances may exhibit complex features, such as a maximum cross-correlation attained at non-collocated locations (dimple or hole effect). Current construction principles for multivariate covariance models on Euclidean spaces do not

A common problem in geostatistics is to interpolate a variable at unsampled locations using available data. Kriging has been the conventional method of solving this problem by providing the weighted average of samples, which is determined by minimizing the estimation variance. Kriging variance is a function of the samples’ spatial configuration and the variable’s spatial dependence structure. The latter

There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus relies on Euclidean geometry and is therefore inappropriate for analysis of point patterns observed in non-Euclidean spaces. Recently, there has been extensions to

In contrast to classical econometric approaches which are based on prespecified isotropic weighting schemes, we suggest that the spatial weighting matrix in the presence of directional dependencies should be estimated. We identify this direction based on different candidate neighbourhood sets. In this paper, we consider two different types of processes – namely spatial autoregressive and spatial autoregressive

Geolocation uncertainty is common in epidemiological studies that depend on addresses to determine exposure. We developed a spatial construct and statistical framework by which to characterize geolocation uncertainty, develop analysis methods, and compare those methods. Exposure is represented by a three-dimensional step function over the partitioned spatial surface and a person’s geolocation boundary

Recent extreme value theory literature has seen significant emphasis on the modelling of spatial extremes, with comparatively little consideration of spatio-temporal extensions. This neglects an important feature of extreme events: their evolution over time. Many existing models for the spatial case are limited by the number of locations they can handle; this impedes extension to space–time settings

Understanding spatial inhomogeneity and clustering in point patterns arises in many contexts, ranging from disease outbreak monitoring to analyzing radiologically-based emphysema in biomedical images. This can often involve classifying individual points as being part of a feature/cluster or as being part of a background noise process. Existing methods for this task can struggle when there are differences

This paper explores the spatial distribution of crime incidences in Nigeria and evaluates the association between the geographical variations and the socio-demographic determinants of crimes. The analyses are based on 2017 reported crime Statistics obtained from the Nigeria‘s National Bureau of Statistics. This paper analysed the spatial patterns of four types of crimes (armed robbery, theft, rape

In this paper, we consider a spatial linear model under the multivariate Student’s t-distribution with finite second moment. This distribution, which contains the normal distribution, offers a more flexible framework for modelling spatial data. We use a reparameterized version of the multivariate Student’s t-distribution, so that the scale matrix corresponds to the covariance matrix of the spatial

In regression models for spatial data, it is often assumed that the marginal effects of covariates on the response are constant over space. In practice, this assumption might often be questionable. In this article, we show how a Gaussian process-based spatially varying coefficient (SVC) model can be estimated using maximum likelihood estimation (MLE). In addition, we present an approach that scales

Model-assisted estimation of forest wood volume is approached exploiting the wall-to-wall information available from satellite data and partial information achieved from airborne laser scanning (ALS) covering a portion of the survey area. If the portion covered by ALS is selected by a probabilistic sampling scheme, two-phase estimators are considered in which the two sources of information are exploited

Many countries have enforced social distancing to stop the spread of COVID-19. Within countries, although the measures taken by governments are similar, the incidence rate varies among areas (e.g., counties, cities). One potential explanation is that people in some areas are more vulnerable to the coronavirus disease because of their worsened health conditions caused by long-term exposure to poor air

We propose a novel class of multiscale spatiotemporal models for multivariate Gaussian data. First, we decompose the multivariate data and the underlying latent process with a novel multivariate multiscale decomposition. This decomposition results in multiscale coefficient matrices with elements that are multiscale approximations of spatial directional derivatives. We then assume that the associated

Stochastic weather generators (SWGs) are digital twins of complex weather processes and widely used in agriculture and urban design. Due to improved measuring instruments, an accurate SWG for high-frequency precipitation is now possible. However, high-frequency precipitation data are more zero-inflated, skewed, and heavy-tailed than common (hourly or daily) precipitation data. Therefore, classical

In the last few decades, sampling theory has been given a substantial boost by the growing availability of geo-referenced finite populations. Unfortunately, geo-referentiation is often incomplete or affected by locational errors for a portion of the units. Spatial sampling methods produce efficient estimates but suffer from consequences of flaws in geo-referentiation. This paper proposes a mixed sampling

In spatial regression analysis, a suitable specification of the mean regression model is crucial for unbiased analysis. Also, to enhance statistical efficiency of the mean regression analysis, we need to suitably account for the underlying spatial correlation structure. In this paper, we focus on selection of an appropriate mean model in spatial regression analysis under a general anisotropic nested

Dendritic spines, which are small protrusions on the dendrites of a neuron, are of interest in neuroscience as they are related to cognitive processes such as learning and memory. We analyse the distribution of spine locations on six different dendrite trees from mouse neurons using point process theory for linear networks. Besides some possible small-scale repulsion, we find that two of the spine

Complex valued random fields, a natural generalization of real valued random fields, represent a powerful tool for modeling phenomena which evolve in time, spatial vectorial data in two dimensions and spatio-temporal vectorial data (i.e., a wind field). However, only a few efforts have been proposed in the literature to address some relevant aspects of spatial and spatio-temporal geostatistical analysis

Although ambulance call data typically come in the form of spatio-temporal point patterns, point process-based modelling approaches presented in the literature are scarce. In this paper, we study a unique set of Swedish spatio-temporal ambulance call data, which consist of the spatial (GPS) locations of the calls (within the four northernmost regions of Sweden) and the associated days of occurrence

In recent years, in many application fields, extracting information from data in the form of functions is of most interest rather than investigating traditional multivariate vectors. Often these functions have complex spatial dependences that need to be accounted for using appropriate statistical analysis. Spatial Functional Statistics presents a fruitful analytics framework for this analysis. The

We consider a random marked tessellation in which the marks are crystal lattice orientations. A natural task is to construct a statistical test to decide whether the orientations are independently assigned to the cells of the underlying tessellation. The distribution of a given orientation is either identical for all cells or may depend on the corresponding cell. For both cases, non-parametric tests

This is the editorial letter for the Special Issue dedicated to the conference Spatial Statistics 2019 Towards Spatial Data Science held in Sitges (Spain) from July 10 to 13, 2019. This fifth international conference on Spatial Statistics was run under the theme Towards Spatial Data Science with the aim to honour the emerging field of Data Science with a focus on spatial and spatio-temporal methods

A motivating example for this paper is a large human location information system that collects two types of information on mobile device locations: 1) large amounts of low-accuracy cell tower triangulation (CTT) calculated location data and 2) small amounts of high-accuracy assisted global positioning system (AGPS) pinpointed location data. Integrating the CTT and AGPS data and extracting more complete

In environmental sciences, it is very common to observe spatio-temporal multiple data concerning several correlated variables which are measured in time over a monitored spatial domain. In multivariate Geostatistics, the evaluation of their behavior is often based on the knowledge of the spatio-temporal multivariate covariance structure. Since this last is often unknown it has to be estimated and modeled

Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analyzing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes does not scale with data volume and requires strong assumptions about stationarity, separability, and distance measures of covariance functions that are often unrealistic

The joint influence of different facilities plays an important role in understanding situational profiles of crime incidents. While spatial conjunctive analysis of case configurations (CACC) is widely used to explore situational profiles of crime, complex spatial interactions (e.g., spatial autocorrelation of crime incidents, spatial interactions among multiple facilities) have not been fully considered

Monitoring of variables like temperature, precipitation, and air quality is performed to determine their current situation, exhibit the presence of trends and occurrence of outliers. These variables are measured at specific locations and to obtain a full estimation map, we need to predict values at unknown locations. This study focuses on making a minimum air temperature map using copula interpolation

Information Theory provides a fundamental basis for analysis, and for a variety of subsequent methodological approaches, in relation to uncertainty quantification. The transversal character of concepts and derived results justifies its omnipresence in scientific research, in almost every area of knowledge, particularly in Physics, Communications, Geosciences, Life Sciences, etc. Information-theoretic

Objective: Road traffic crashes (RTCs) are a major global public health problem and cause substantial burden on national economy and healthcare. There is little systematic understanding of the geography of RTCs and the spatial correlations of RTCs in the Middle-East region, particularly in Oman where RTCs are the leading cause of disability-adjusted life years lost. The overarching goal of this paper

In some applications, clustered survival data are arranged spatio-temporally such as geographical regions over multiple time periods. Incorporating spatio-temporal variation in these data not only can improve the accuracy and efficiency of parameter estimation, but it also investigates spatial pattern of survivorship over the study period for identifying high-risk areas. Competing risks in survival

Identifying poverty determinants in a region is crucial for taking effective poverty reduction measures. This paper utilizes two variable importance analysis methods to identify the relative importance of different geographic factors to explain the spatial distribution of poverty: the Lindeman, Merenda, and Gold (LMG) method used in multiple linear regression (MLR) and variable importance used in random

Various methods for directional analysis of spatial point patterns have been introduced in the literature. In this paper, we formulate a unifying framework for methods based on integral transforms of the second order product density. Examples include directional versions of Ripley’s K-function, wavelet transforms, and spectral analysis. Furthermore, we propose an additional method based on the projection

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to spatial point processes. While the original embedding is infinite-dimensional and implicit, our approximate embedding is finite-dimensional and comes with explicit

In lattice type of spatial data analysis, the choice of spatial weighting matrices is a main component of any spatial autocorrelation measures and spatial autoregressive models because the choice assumes priori structures of spatial dependency. Typically, weighting matrices are constructed based on the concept of spatial proximity or geographical distance-based functions. However, depending on the

Images are particular and well–known instances of spatial big data. Typically spatial data are scale specific and in this paper, we propose mechanisms to effectively address issues of scale in the analysis of images. We focus on spatial data extracted from images using the Discrete Pulse Transform (DPT). The DPT extracts discrete pulses from images at multiple scales that are recognisable as connected

This paper proposes a new class of covariance functions for bivariate random fields on spheres, having the same properties as the bivariate Matérn model proposed in Euclidean spaces. The new class depends on the geodesic distance on a sphere; it allows for indexing differentiability (in the mean square sense) and fractal dimensions of the components of any bivariate Gaussian random field having such

Under the realization that Geographically Weighted Regression (GWR) is a data-borrowing technique, this paper derives expressions for the amount of bias introduced to local parameter estimates by borrowing data from locations where the processes might be different from those at the regression location. This is done for both GWR and Multiscale GWR (MGWR). We demonstrate the accuracy of our expressions

Let x={x(1),…,x(n)} be a space filling-design of n points defined in 0,1d. In computer experiments, an important property seek for x is a nice coverage of 0,1d. This property could be desirable as well as for any projection of x onto 0,1ι for ι

In this paper, we develop a method for estimating and clustering two-dimensional spectral density functions (2D-SDFs) for spatial data from multiple subregions. We use a common set of adaptive basis functions to explain the similarities among the 2D-SDFs in a low-dimensional space and estimate the basis coefficients by maximizing the Whittle likelihood with two penalties. We apply these penalties to

This paper proposes a Bayesian method for spatial regression using eigenvector spatial filtering (ESF) and Piironen and Vehtari (2017)’s regularized horseshoe (RHS) prior. ESF models are most often estimated using variable selection procedures such as stepwise selection, but in the absence of a Bayesian model averaging procedure variable selection methods cannot properly account for parameter uncertainty

A non-stationary Gaussian random field model is developed based on a combination of the stochastic partial differential equation (SPDE) approach and the classical deformation method. With the deformation method, a stationary field is defined on a domain which is deformed so that the field becomes non-stationary. We show that if the stationary field is a Matérn field defined as a solution to a fractional

In Geostatistics, vector data with two components, such as measures for wind field, electromagnetic field and ocean currents can be appropriately modeled by recalling the theory of complex-valued random fields. This is especially suitable for describing phenomena whose variables are expressed in the same unit of measurement and refer to homogeneous quantities. In this paper, a first approach useful

Citizen Scientists together with an increasing access to technology provide large datasets that can be used to study e.g. ecology and biodiversity. Unknown and varying sampling effort is a major issue when making inference based on citizen science data. In this paper we propose a modeling approach for accounting for variation in sampling effort due to accessibility. The paper is based on an illustrative

The object of this work is to predict the seismic rate in Chile by using two Deep Neural Network (DNN) architectures, Long Short Term Memory (LSTM) and Convolutional Neural Networks (CNN). For this, we propose a methodology based on a three-module approach: a pre-processing module, a spatial and temporal estimation module, and a prediction module. The first module considers the Epidemic-Type Aftershock