Major infectious diseases such as COVID-19 have a significant impact on population lives and put enormous pressure on healthcare systems globally. Strong interventions, such as lockdowns and social distancing measures, imposed to prevent these diseases from spreading, may also negatively impact society, leading to jobs losses, mental health problems, and increased inequalities, making crucial the prioritization

Rich new marked point process data allow researchers to consider disparate problems such as the factors affecting the location and type of police use of force incidents, and the characteristics that impact the location and size of forest fires. We develop a two-stage log Gaussian Cox process that models these data in terms of both spatial (community-level) and nonspatial (individual or event-level)

The modifiable areal unit problem (MAUP) refers to the effects caused by modifying the units of analysis in the context of spatial statistical analyses on areal data. The problem was formulated decades ago, but it is still of interest due to its complexity. Usually, studies on the MAUP are experimental, focusing mainly on analyzing the variation of model estimates or statistical properties as a consequence

Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace-variogram, which quantifies spatial variation, can be misleading when analyzing misaligned functional data with phase variation. To remedy this, we describe a framework that extends amplitude-phase separation methods in functional data to the spatial setting, with a view

In this paper, an extended mixed geographically and temporally weighted regression (EMixed-GTWR) model is proposed to capture the fusion of the temporal stationarity and spatio-temporal heterogeneity in a regression relationship. A residual-based bootstrap test method is introduced to detect the spatially varying coefficients in a geographically and temporally weighted regression (GTWR) model. Since

This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the process are available at the spatial sites, this method avoids assumptions like isotropy, which are not valid in many applications. As part of the derivations, new nonparametric

School-based sampling has been used to inform targeted responses for malaria and neglected tropical diseases. Standard geostatistical methods for mapping disease prevalence use the school location to model spatial correlation, which is questionable since exposure to the disease is more likely to occur in the residential location. In this paper, we propose to overcome the limitations of standard geostatistical

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial extreme value theory based on the conditional multivariate extreme value model, whereby the limit theory is formed through conditioning upon the value at a particular

Preferential sampling provides a formal modeling specification to capture the effect of bias in a set of sampling locations on inference when a geostatistical model is used to explain observed responses at the sampled locations. In particular, it enables modification of spatial prediction adjusted for the bias. Its original presentation in the literature addressed assessment of the presence of such

In this paper, I show how neural networks can be used to simultaneously estimate all unknown parameters in a spatial point process model from an observed point pattern. The method can be applied to any point process model which it is possible to simulate from. Through a simulation study, I conclude that the method recovers parameters well and in some situations provide better estimates than the most

In this work, we develop a constructive modeling framework for extreme threshold exceedances in repeated observations of spatial fields, based on general product mixtures of random fields possessing light or heavy-tailed margins and various spatial dependence characteristics, which are suitably designed to provide high flexibility in the tail and at sub-asymptotic levels. Our proposed model is akin

Analyzing population representative datasets for local level estimation and prediction purposes is important for monitoring public health, however, there are many statistical challenges associated with such analyses. Small area estimation (SAE) with post-stratified hierarchical mixed-effects models is a popular method for analysis. Post-stratification is a method that creates area-level predictions

Spatial autocorrelation and spatial heterogeneity are fundamental properties of geo-referenced data. Spatial autoregressive varying coefficient models have been proposed to simultaneously deal with spatial autocorrelation in the response variable and spatial heterogeneity in the regression relationship. Nevertheless, the identification of spatial heterogeneity in the spatial lag term and in the regression

This paper presents a spatial process with covariate-dependent random joint distributions. Our construction is based on an extension of the Gaussian copula model using the Beta-regression process. As a generalized form of stick-breaking processes, the proposed model allows the covariance function to be covariate-driven nonstationary. Also, the resulting labeling process provides a covariate-dependent

Ground pressure and temperature are two key meteorological parameters for retrieving precipitable water vapor (PWV) from Global Navigation Satellite Systems (GNSS). The problem is that, many GNSS stations are either not equipped with meteorological sensors or the time resolution of meteorological data is relatively low. To improve the spatio-temporal resolution of meteorological parameters, a new spatio-temporal

The difference between potential and actual distribution of species is emphasized, pointing out the ecological importance of providing maps that depict the actual species presence on the study region. Owing to the impossibility of performing complete surveys over large areas, the presence/absence of species at a pre-fixed spatial grain is estimated for any location of the study region from the presences/absences

We present a general statistical methodology for analysing a Laguerre tessellation data set viewed as a realization of a marked point process model. In the first step, for the points, we use a nested sequence of multiscale processes which constitute a flexible parametric class of pairwise interaction point process models. In the second step, for the marks/radii conditioned on the points, we consider

Spatially varying coefficient (SVC) regression models are concerned about regression for spatial data, where regression coefficients may vary in space. This paper proposes a new approach for SVC modeling by representing regression coefficients using a class of multiresolution spline basis functions in a generalized-linear model framework. The proposed method provides flexible and parsimonious representations

This paper introduces a K-function for assessing second-order properties of inhomogeneous random measures generated by marked point processes. The marks can be geometric objects like fibers or sets of positive volume, and the presented K-function takes into account geometric features of the marks, such as tangent directions of fibers. The K-function requires an estimate of the inhomogeneous density

Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close to a semiparametric one. Motivated by eye-movement data, we introduce a convolution type model where the log-intensity is modelled as the convolution of a function

Different spatial point process models and techniques have been developed in the past decades to facilitate the statistical analysis of spatial point patterns. However, in some cases the spatial point process methodology is scarce and no flexible models nor suitable statistical methods are available. For example, due to its complexity, the statistical analysis of spatial point patterns of several groups

This paper summarizes the development and application of spatial statistical models in satellite optical remote sensing. The paper focuses on the development of a conceptual model that includes the measurement and sampling processes inherent in remote sensing. We organized this paper into five main sections: introducing the basis of remote sensing, including measurement and sampling; spatial variation

We propose a flexible model for a partially migrating species, which we demonstrate using yearly paths for golden eagles (Aquila chrysaetos). Our model relies on a smoothly time-varying potential surface defined by a number of attractors. We compare our proposed approach using varying coefficients to a latent-state model, which we define differently for migrating, dispersing, and local individuals

For the better part of the 20th century pedologists mapped soil by drawing boundaries between different classes of soil which they identified from survey on foot or by vehicle, supplemented by air-photo interpretation, and backed by an understanding of landscape and the processes by which soil is formed. Its limitations for representing gradual spatial variation and predicting conditions at unvisited

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on γ-divergence. A novel feature of the proposed approach is that two tuning parameters that control robustness and spatial smoothness are automatically tuned in a data-dependent manner. Further, the proposed method

We propose a new estimation method to fit a semiparametric intensity function model to multivariate spatial point processes. Our approach is based on the so-called quasi-likelihood that can produce more efficient estimators by accounting for both between- and within-process correlations. To be more specific, we derive the optimal estimating function in a class of first-order estimating functions, where

The estimation of range parameters for spatial covariance functions has long been a source of theoretical and practical problems in spatial statistics. In particular, in many applications, one finds that likelihood and, especially, restricted likelihood functions, do not provide any meaningful upper bound on the range parameter of a parametric covariance function model. This work seeks to provide further

This work focuses on variable selection for spatial regression models, with locations on irregular lattices and errors according to Conditional or Simultaneous Auto-Regressive (CAR or SAR) models. The strategy is to whiten the residuals by estimating their spatial covariance matrix and then proceed by performing the standard L1-penalized regression LASSO for independent data on the transformed model

This work proposes a novel approach to the calibration of regionalized regression models, with particular reference to ground-motion models (GMMs), which are key for probabilistic seismic hazard analysis and earthquake engineering applications. A novel methodology, named multi-source geographically-weighted regression (MS-GWR), is developed, allowing one to (i) estimate regionalized regression models

Spatial disease modeling remains an important public health tool. For cholera, the presence of zero counts is common. The Poisson model is inadequate to (1) capture over-dispersion, and (2) distinguish between excess zeros arising from non-susceptible and susceptible populations. In this study, we develop zero-inflated (ZI) mixture spatially varying coefficient (SVC) models to (1) distinguish between

Poverty affects many people worldwide and varies in space and time, although its determinants are geographical factors. This paper presents a case study from Hubei Province, Central China, investigating the spatial and temporal changes in poverty determinants at the county and village levels from 2013 to 2017. We investigated the variation in the spatial autocorrelation of poverty incidence at the

Measures of local and global spatial association are key tools for exploratory spatial data analysis. Many such measures exist including Moran’s I, Geary’s C, and the Getis–Ord G and G∗ statistics. A parametric approach to testing for significance relies on strong assumptions, which are often not met by real world data. Alternatively, the most popular nonparametric approach, the permutation test, imposes

Over the past two decades increasing focus has been given to local forms of spatial analysis, both in terms of descriptive statistics and spatial modeling. We term this “thinking locally” Fundamental to thinking locally is that a global approach to spatial analysis may not be suitable and that there may be situations where the conditioned relationships we want to measure vary over space. This paper

Recent years have seen an increased interest in the application of methods and techniques commonly associated with machine learning and artificial intelligence to spatial statistics. Here, in a celebration of the ten-year anniversary of the journal Spatial Statistics, we bring together normalizing flows, commonly used for density function estimation in machine learning, and spherical point processes

When the sampled population belongs to a metric space, the selection of neighboring units will imply often similarities in the collected data due to their geographical proximity. In order to estimate parameters such as means or totals, it is therefore more efficient to select samples that are well distributed in space. Often, the interest lies not only in estimating a parameter at one point in time

Mining activities depend significantly on water resources availability as it consists a major tool of the extraction, processing and the post closure mining operations. Especially, groundwater is the major water source in most mining areas. However, overexploitation, competition from the communities and climate change effects have caused significant stress on the groundwater resources in many areas

Finding cause–effect relationships behind observed phenomena remains a challenge in spatial analysis. In recent years, much progress in causal inference has been made in statistics, economics, epidemiology and computer sciences, but limited progress has been made in spatial statistics due to the nonrandom, nonrepeatability and synchronism of spatial data. In this paper, we investigate the problem.

Satellite remote sensing data are important to the study of environment problems at a global scale. The GloboLakes project aimed to use satellite remote sensing data to investigate the response of the major lakes on Earth to environmental conditions and change. The main challenge to statistical modelling is the identification of the spatial structure in global lake ecological processes from a large

In this paper we review approaches which have been taken to characterizing the uncertainty in spatial information. This includes both continuous predictions of spatial variables, and thematic maps of landcover classes. We contend that much work in this area has failed to engage adequately with the decision processes of the end-user of information, and that the engagement of spatial statisticians is

COVID–19 incidence is analyzed at the provinces of the Spanish Communities in the Iberian Peninsula during the period February–October, 2020. Two infinite–dimensional regression approaches, surface regression and spatial curve regression, are proposed. In the first one, Bayesian maximum a posteriori (MAP) estimation is adopted in the approximation of the pure point spectrum of the temporal regression

Surveying programs of study at institutions of higher learning throughout the world reveals that one natural disciplinary coupling is statistics and operations research, although these two specific disciplines currently lack an active synergistic research interface. Similarly, the development of spatial statistics and spatial optimization has occurred in parallel and nearly in isolation. This paper

Spectral methods are important for both theory and computation in spatial data analysis. When data lie on a grid, spectral approaches can take advantage of the discrete Fourier transform for fast computation. If data are not on a grid, then low-rank processes with Fourier basis functions may be sufficient approximations. However, deciding which basis functions to use is difficult and can depend on

This article gives a narrative overview of what constitutes climatological data and their typical features, with a focus on aspects relevant to statistical modeling. We restrict the discussion to univariate spatial fields and focus on maximum likelihood estimation. To address the problem of enormous datasets, we study three common approximation schemes: tapering, direct misspecification, and composite

Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert spaces, and graph based models. This article describes how the stochastic partial differential equation approach to generalising Matérn covariance models via Hilbert

The main determinants of COVID-19 spread in Italy are investigated, in this work, by means of a D-vine copula based quantile regression. The outcome is the COVID-19 cumulative infection rate registered on October 30th 2020, with reference to the 107 Italian provinces, and it is regressed on some covariates of interest accounting for medical, environmental and demographic factors. To deal with the issue

The individual observations used to estimate spatial regression models often constitute only a sample of the theoretically observable data points. In many cases, such a sample does not obey a specific design and it is collected only with convenience criteria as it happens, e.g. when data are web scraped or crowdsourced. Thus, we expect to observe possible biases and inefficiencies while estimating

The theory of complex-valued random fields was already used in Geostatistics to describe vector data with two components. However, in the literature, there are various contributions focused only on modeling their spatial evolution, while the temporal perspective was analyzed separately or used to model time-varying complex covariance models. Thus, in this context it is surely challenging to propose

We discuss recent methodological developments in inhomogeneous summary statistics and envelope testing and study their applications in the field of spatial point pattern analysis. Specifically, we use these methods to test McGill’s theory of biodiversity. This theory is based upon three axioms: individuals of the same species cluster together, many rare species co-exist with a few common ones and individuals

On the occasion of the Spatial Statistics’ 10th Anniversary, I reflect on the past and present of Bayesian disease mapping and look into its future. I focus on some key developments of models, and on recent evolution of multivariate and adaptive Gaussian Markov random fields and their impact and importance in disease mapping. I reflect on Bayesian disease mapping as a subject of spatial statistics

Species distribution modeling is a primary ecological activity that has witnessed substantial evolution since the turn of the 21st century. For plant communities, two key features are the move from individual to joint species modeling and the move from regression modeling assuming independence across sites to the introduction of spatial structure across sites. The latter transition has also illuminated

The Stochastic Partial Differential Equation (SPDE) approach, now commonly used in spatial statistics to construct Gaussian random fields, is revisited from a mechanistic perspective based on the movement of microscopic particles, thereby relating pseudo-differential operators to dispersal kernels. We first establish a connection between Lévy flights and PDEs involving the Fractional Laplacian (FL)

Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar than the ones further separated. This might hold also true for cross-dependencies when multivariate spatial data is considered. Often, scientists are interested in

Sea ice plays a significant role in global climate change. Marginal ice zone (MIZ) is defined as the transition zone between open ocean and pack ice where intensive air-ice-ocean-wave interactions between the ocean and the atmosphere occur. This definition of MIZ is rather vague, which affects its mapping. Previous data-driven methods extracted MIZ from single source data and conveniently used a single

In the United States, COVID-19 has become a leading cause of death since 2020. However, the number of COVID-19 deaths reported from death certificates is likely to represent an underestimate of the total deaths related to SARS-CoV-2 infections. Estimating those deaths not captured through death certificates is important to understanding the full burden of COVID-19 on mortality. In this work, we explored

Georeferenced compositional data are prominent in many scientific fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose, a novel class of α-transformations, named the Isometric α-transformation (α-IT), is proposed, which encompasses the traditional Isometric Log-Ratio (ILR) transformation

This paper presents an overview of the journal Spatial Statistics. It describes how it was initiated, how it developed and it highlights key moments from its young history. Starting in 2012, the journal has progressed in conjunction with the series of conferences in different countries over five continents. An important moment occurred when the journal received an impact factor in 2014. After a decline