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

A large number of approaches for modelling spatially dependent functional variables often assume that the functional regression coefficients are constant over the region of interest. However, in many occasions it is far more realistic that functional coefficients vary at a local level. The present paper proposes a calibrated heteroskedastic geographically weighted regression model (H-GWR) in the functional

Nonparametric resampling methods such as Direct Sampling are powerful tools to simulate new datasets preserving important data features such as spatial patterns from observed datasets while using only minimal assumptions. However, such methods cannot generate extreme events beyond the observed range of data values. We here propose using tools from extreme value theory for stochastic processes to extrapolate

For a given region, we have a dataset composed of car theft locations along with a linked dataset of recovery locations which, due to partial recovery, is a relatively small subset of the set of theft locations. For an investigator seeking to understand the behavior of car thefts and recoveries in the region, several questions are addressed. Viewing the set of theft locations as a point pattern, can

This study investigates the propagation power and effects of the coronavirus disease 2019 (COVID-19) in light of published data. We examine the factors affecting COVID-19 together with the spatial effects, and use spatial panel data models to determine the relationship among the variables including their spatial effects. Using spatial panel models, we analyse the relationship between confirmed cases

Issues on sampling procedure definition led numerous study results to be biased and object of controversy. Choosing relevant sampling design and number of samples is a difficult task when wanted to set up or optimize a survey. The survey design choice is very important to avoid bias and increase the survey cost-efficiency. It can have a strong effect on the sample size needed to achieve some targeted

Building clusters for pattern recognition and analysis of geographical areas can be a useful way to provide relevant information for economic and social decisions. In this paper, we introduce a novel spatial clustering technique, called Bootstrap ClustGeo (BCG), which is a hierarchical approach, based on bootstrap techniques with spatial constraints. We evaluate the performance of the proposed approach

This paper analyzes the spatiotemporal pattern of gunfire reports collected by the collaborative mobile app Fogo Cruzado in the Rio de Janeiro metropolitan area (Brazil). We apply nonparametric first and second-order inference tools to characterize gunfire behavior, and test whether gunfire patterns meet the assumptions of crime prediction models, such as kernel hotspot maps or self-exciting point

Workers around the world spend nearly a quarter of their time at work Occupational health is gaining great importance due to the profound impact on people long term health. The health status of the primary sector workforce is a great unknown for medical geography where health maps and spatial patterns have not been able to explain years of changing disease rates. This article proposes a new approach

We review recent research on statistical methods for analysing spatial patterns of points on a network of lines, such as road accident locations along a road network. Due to geometrical complexities, the analysis of such data is extremely challenging, and we describe several common methodological errors. The intrinsic lack of homogeneity in a network militates against the traditional methods of spatial

Testing for a covariate effect in a parametric point process model is usually done through the Wald test, which relies on an asymptotic null distribution of the test statistic. We propose a Monte Carlo version of the test that also allows local investigation of the covariate effect in the globally fitted model. Two different test statistics are suggested for this purpose: the first, a spatial statistic

Due to climate change and human activity, wildfires are expected to become more frequent and extreme worldwide, causing economic and ecological disasters. The deployment of preventive measures and operational forecasts can be aided by stochastic modeling that helps to understand and quantify the mechanisms governing the occurrence intensity. We here develop a point process framework for wildfire ignition

Diagnosis is often based on the exceedance or not of continuous health indicators of a predefined cut-off value, so as to classify patients into positives and negatives for the disease under investigation. In this paper, we investigate the effects of dichotomization of spatially-referenced continuous outcome variables on geostatistical inference. Although this issue has been extensively studied in

Mixed models are commonly used to analyze spatial data which frequently occur in practice such as in health sciences and life studies. It is customary to incorporate spatial random effects into the model to account for spatial variation of the data. In particular, Poisson mixed models are used to analyze spatial count data. It is often assumed that the observations in each area, conditional on the

We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become the standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality

The scope of spatial statistics problems arising in ecology is substantial. They concern both plant and animal behavior. Here, we discuss only plants. The range of issues is still very large and so we confine ourselves to four challenges, each within the context of model development. These are: species distribution models, both individual and joint; preferential sampling and bias in presence/absence

In the age of big data, imaging techniques such as imaging mass spectrometry (IMS) stand out due to the combination of data size and spatial referencing. However, the data analytic tools readily accessible to investigators often ignore the spatial information or provide results with vague interpretations. We focus on imaging techniques like IMS that collect data along a regular grid and develop methods

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has

We clear land for agricultural purposes, we draw water from streams and aquifers, and we build houses in coastal regions for their ready access to the sea. Our need for food, water, and shelter is basic, but so is variability in our natural environment. Understanding this is key to the long-term sustainability of the anthropocene. At any location in the environment, long-term temporal averages may

When data for observations are missing, scientists often remove those observations from an analysis, or replace them with imputations, with few other options available to these analysts. Confining an analysis to those observations with complete data can waste resources expended for, especially, those observations with near-complete data. Selectively retaining variables with complete data for observations

We focus on the discussion of modeling processes that are observed at fixed locations of a region (geostatistics). A standard approach is to assume that the process of interest follows a Gaussian Process with some mean and (valid) covariance functions. It is common to model the covariance function as the product between a variance parameter, and a correlation function which is a function of the Euclidean

Statistical analysis of spatio-temporal data has been evolving to handle increasingly large data sets. For example, the North American CORDEX program is producing daily values of climate-related variables on spatial grids with approximately 100,000 locations over 150 years. Smoothing of such massive and noisy data is essential to understanding their spatio-temporal features. It also reduces the size

The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics is the design of the locations of the monitoring stations for those environmental processes of interest. One particular design criterion for monitoring networks that

In multivariate spatio-temporal analysis, we are faced with the formidable challenge of specifying a valid spatio-temporal cross-covariance function, either directly or through the construction of processes. This task is difficult as these functions should yield positive definite covariance matrices. In recent years, we have seen a flourishing of methods and theories on constructing spatio-temporal

Hazard assessment at a regional scale may be performed thanks to a spatial model for maxima that can be obtained by combining the generalized extreme-value (GEV) distribution for the univariate marginal distributions with extreme-value copulas to describe their dependence structure, as justified by the theory of multivariate extreme values. A flexible class of extreme-value copulas, called XGumbel

Integro-difference equation (IDE) models describe the conditional dependence between the spatial process at a future time point and the process at the present time point through an integral operator. Nonlinearity or temporal dependence in the dynamics is often captured by allowing the operator parameters to vary temporally, or by re-fitting a model with a temporally-invariant linear operator in a sliding

A suite of statistical methods are used to study animal movement. Most of these methods treat animal telemetry data in one of three ways: as discrete processes, as continuous processes, or as point processes. We briefly review each of these approaches and then focus in on the latter. In the context of point processes, so-called resource selection analyses are among the most common way to statistically

The application of geostatistical and machine learning methods based on Gaussian processes to big space–time data is beset by the requirement for storing and numerically inverting large and dense covariance matrices. Computationally efficient representations of space–time correlations can be constructed using local models of conditional dependence which can reduce the computational load. We formulate

In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to compare two spatial sequences along a 45°line. The proposed coefficient was explored for the bivariate Matérn and Wendland covariance functions. The asymptotic normality

The paper uses two case-studies, one in public health surveillance the other in veterinary epidemiology, to argue that the analysis strategy for spatio-temporal point process data should be guided by the scientific context in which the data were generated and, more particularly, by the objectives of the data analysis. This point of view is not specific to the point process setting and, in the author’s

Aside from reviewing different intensity estimation schemes for point processes on linear networks, this paper introduces two Voronoi-based intensity estimation approaches for spatio-temporal linear network point processes. The first is a separable estimator, which is obtained as a scaled product of a resample-smoothed Voronoi intensity estimator on the linear network in question and another one on

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order interactions. However, until recently, there has been a strong reliance on a limited class of stationary kernels such as the Matérn or squared exponential, limiting

Glaucoma disease progression, as measured by visual field (VF) data, is often defined by periods of relative stability followed by an abrupt decrease in visual ability at some point in time. Determining the transition point of the disease trajectory to a more severe state is important clinically for disease management and for avoiding irreversible vision loss. Based on this, we present a unified statistical

Pulmonary emphysema is a destructive disease of the lungs that is currently diagnosed via visual assessment of lung Computed Tomography (CT) scans by a radiologist. Visual assessment can have poor inter-rater reliability, is time consuming, and requires access to trained assessors. Quantitative methods that reliably summarize the biologically relevant characteristics of an image are needed to improve

Our work is motivated by a desire to incorporate the vast wealth of social network data into the framework of spatial models. We introduce a method for modeling the spatial correlations that exist over a social network. In particular, we model attributes measured for each member of the network as a continuous process over the social space created by their connections. Our method simultaneously models

Spatially-referenced geostatistical responses that are collected in environmental sciences research are often subject to detection limits, where the measures are not fully quantifiable. This leads to censoring (left, right, interval, etc), and various ad hoc statistical methods (such as choosing arbitrary detection limits, or data augmentation) are routinely employed during subsequent statistical analysis

This paper investigates the adequacy of the matrix exponential spatial specifications (MESS) as an alternative to the widely used spatial autoregressive models (SAR). To provide as complete a picture as possible, we extend the analysis to all the main spatial models governed by matrix exponentials comparing them with their spatial autoregressive counterparts. We propose a new implementation of Bayesian

Obtaining reliable estimates about health outcomes for areas or domains where only few to no samples are available is the goal of small area estimation (SAE). Often, we rely on health surveys to obtain information about health outcomes. Such surveys are often characterised by a complex design, stratification, and unequal sampling weights as common features. Hierarchical Bayesian models are well recognised

Individual-level data from the Florida Cancer Data System (1981-2007) were analysed to explore temporal trends of prostate cancer late-stage diagnosis, and how they vary based on race, income and age. Annual census-tract rates were computed for two races (white and black) and two age categories (40-65, >65) before being aggregated according to census tract median household incomes. Joinpoint regression

We present a methodology that detects event aggregation about a mass surface using 3-dimensional study regions with a point pattern and a mass present. The Aggregation about a Mass function determines aggregation, randomness, or repulsion of events with respect to the mass surface. Our method closely resembles Ripley's K function but is modified to discern the pattern about the mass surface. We briefly

This paper develops a hierarchical framework for identifying spatiotemporal patterns in data with a high degree of censoring using the gradient process. To do this, we impute censored values using a sampling-based inverse CDF method within our Markov chain Monte Carlo algorithm, thereby avoiding burdensome integration and facilitating efficient estimation of other model parameters. We illustrate use

Small area estimation (SAE) is an important endeavor in many fields and is used for resource allocation by both public health and government organizations. Often, complex surveys are carried out within areas, in which case it is common for the data to consist only of the response of interest and an associated sampling weight, reflecting the design. While it is appealing to use spatial smoothing models

The accurate assessment of exposure to ambient ozone concentrations is important for informing the public and pollution monitoring agencies about ozone levels that may lead to adverse health effects. High-resolution air quality information can offer significant health benefits by leading to improved environmental decisions. A practical challenge facing the U.S. Environmental Protection Agency (USEPA)

In applications where covariates and responses are observed across space and time, a common goal is to quantify the effect of a change in the covariates on the response while adequately accounting for the spatio-temporal structure of the observations. The most common approach for building such a model is to confine the relationship between a covariate and response variable to a single spatio-temporal

This short paper is centered on hierarchical modeling for problems in spatial and spatio-temporal statistics. It draws its motivation from the interdisciplinary research work of the author in terms of applications in the environmental sciences - ecological processes, environmental exposure, and weather modeling. The paper briefly reviews hierarchical modeling specification, adopting a Bayesian perspective

The current work provides a nonparametric resampling procedure for approximating the (unconditional) probability that a spatial variable surpasses a prefixed threshold value. The existing approaches for the latter issue require assuming constant variance throughout the observation region, thus our proposal has been designed to be valid under heteroscedasticity of the spatial process. To develop the

It is widely accepted that spatial dependencies have to be acknowledged appropriately in data that are spatially aligned. However, most spatial models still assume that the dependence structure does not vary over space, i.e., it is stationary. While assuming stationarity considerably facilitates estimation, it is often too restrictive when describing atmospheric phenomena such as precipitation. Nonetheless

Multivariate disease mapping models are attracting considerable attention. Many modeling proposals have been made in this area, which could be grouped into three large sets: coregionalization, multivariate conditional and univariate conditional models. In this work we establish some links between these three groups of proposals. Specifically, we explore the equivalence between the two conditional approaches

This paper addresses the problem of comparing the spatial distribution of two point patterns. A formal statistical test is proposed to decide whether two observed patterns share the same theoretical intensity model. This underlying model assumes that the first-order intensity function of the process generating the patterns may depend on covariate information. The test statistic consists of an L2-distance