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AbstractSpatial time series (STS), which refers to time-series data collected at fixed spatial locations, is crucial for understanding the spatiotemporal dynamics of geographical phenomena. Measuring the spatial association based on STS similarity provides valuable insights into the exploratory analysis of spatiotemporal data. However, existing methods are not effective in accurately quantifying such spatial association. To address this gap, this study proposes a conceptual model and a statistical method for identifying spatial clusters that exhibit significantly similar time-varying characteristics within a set of STS data. Conceptually, three representative patterns are defined: positive, negative, and no associations. A positive pattern occurs when spatially adjacent STSs show similar time-varying characteristics, while a negative pattern occurs when they show dissimilar ones. Technically, this study introduces a distance metric to measure similarities among STSs. The spatial association of STS at global and local scales is quantified according to the spatial concentration of these similarities. The validity and applicability of the proposed statistics are verified through synthetic and real-world examples, demonstrating their potential as effective tools for understanding spatiotemporal dynamics from a new perspective. [ABSTRACT FROM AUTHOR]

Clusters of similar or dissimilar objects are encountered in many fields. Frequently used approaches treat each cluster's central object as latent. Yet, often objects of one or more types cluster around objects of another type. Such arrangements are common in biomedical images of cells, in which nearby cell types likely interact. Quantifying spatial relationships may elucidate biological mechanisms. Parent‐offspring statistical frameworks can be usefully applied even when central objects ("parents") differ from peripheral ones ("offspring"). We propose the novel multivariate cluster point process (MCPP) to quantify multi‐object (e.g., multi‐cellular) arrangements. Unlike commonly used approaches, the MCPP exploits locations of the central parent object in clusters. It accounts for possibly multilayered, multivariate clustering. The model formulation requires specification of which object types function as cluster centers and which reside peripherally. If such information is unknown, the relative roles of object types may be explored by comparing fit of different models via the deviance information criterion (DIC). In simulated data, we compared a series of models' DIC; the MCPP correctly identified simulated relationships. It also produced more accurate and precise parameter estimates than the classical univariate Neyman–Scott process model. We also used the MCPP to quantify proposed configurations and explore new ones in human dental plaque biofilm image data. MCPP models quantified simultaneous clustering of Streptococcus and Porphyromonas around Corynebacterium and of Pasteurellaceae around Streptococcus and successfully captured hypothesized structures for all taxa. Further exploration suggested the presence of clustering between Fusobacterium and Leptotrichia, a previously unreported relationship. [ABSTRACT FROM AUTHOR]

In geostatistics, traditional spatial models often rely on the Gaussian process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes, necessitating the use of approximate methods. A powerful class of methods approximate the GP as a sum of basis functions with random coefficients. Although this technique offers computational efficiency, it does not inherently guarantee a stationary covariance. To mitigate this issue, the basis functions can be ‘normalized’ to maintain a constant marginal variance, avoiding unwanted artefacts and edge effects. This allows for the fitting of nearly stationary models to large, potentially non‐stationary datasets, providing a rigorous base to extend to more complex problems. Unfortunately, the process of normalizing these basis functions is computationally demanding. To address this, we introduce two fast and accurate algorithms to the normalization step, allowing for efficient prediction on fine grids. The practical value of these algorithms is showcased in the context of a spatial analysis on a large dataset, where significant computational speedups are achieved. While implementation and testing are done specifically within the LatticeKrig framework, these algorithms can be adapted to other basis function methods operating on regular grids. [ABSTRACT FROM AUTHOR]

Identifying the dynamics of domestic open spaces remains a challenging task. This research applies an adjusted theoretical framework of activity areas to characterize domestic open spaces in the 14th–16th century a.d. in Old Dongola, Sudan. Activity areas were defined as sedimentations of residues of recurring cycles of changing actions rather than stable components of space. To identify domestic space, this research utilizes high-resolution methods: analyses of multiple chemical elements, spatial distribution of objects, and botanical remains of courtyard occupational surfaces, combined with spatial statistics using local Moran's I autocorrelation. The relationships between the remains of human and non-human actions are discussed in terms of the material affordances affecting their deposition within the archaeological layers. Application of these methods allowed for the identification of areas of domestic tasks related to high concentrations of elements, as well as clusters of tools located on their edges. Botanical data corroborated often vague identifications of activities based on geochemistry. [ABSTRACT FROM AUTHOR]

Geostatistics is concerned with the estimation and prediction of spatially continuous phenomena using data obtained at a discrete set of locations. In geostatistics, preferential sampling occurs when these locations are not independent of the latent spatial field, and common modeling approaches that do not account for such a dependence structure might yield wrong inferences. To overcome this issue, some methods have been proposed to model data collected under preferential sampling. However, while these methods assume a constant degree of preferentiality, real data may present a degree of preferentiality that varies over space. For that reason, we propose a new model that accounts for preferential sampling by including a spatially varying coefficient that describes the dependence strength between the process that models the sampling locations and the latent field. To do so, we approximate the preferentiality component by a set of basis functions with the corresponding coefficients being estimated using the integrated nested Laplace approximation (INLA) method. By doing that, we allow the degree of preferentiality to vary over the domain with low computational burden. We assess our model performance by means of a simulation study and use it to analyze the average PM 2.5 levels in the USA in 2022. We conclude that, given enough observed events, our model, along with the implemented inference routine, retrieves well the latent field itself and the spatially varying preferentiality surface, even under misspecified scenarios. Also, we offer guidelines for the specification and size of the set of basis functions. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

Many spatially dependent phenomena that are of interest in environmental problems are characterized by strong anisotropy and non‐stationarity. Moreover, the data are often observed over regions with complex conformations, such as water bodies with complicated shorelines or regions with complex orography. Furthermore, the distribution of the data locations may be strongly inhomogeneous over space. These issues may challenge popular approaches to spatial data analysis. In this work, we show how we can accurately address these issues by spatial regression with differential regularization. We model the spatial variation by a Partial Differential Equation (PDE), defined upon the considered spatial domain. This PDE may depend upon some unknown parameters that we estimate from the data through an appropriate profiling estimation approach. The PDE may encode some available problem‐specific information on the considered phenomenon, and permit a rich modeling of anisotropy and non‐stationarity. The performances of the proposed approach are compared to competing methods through simulation studies and real data applications. In particular, we analyze rainfall data over Switzerland, characterized by strong anisotropy, and oceanographic data in the Gulf of Mexico, characterized by non‐stationarity due to the Gulf Stream. [ABSTRACT FROM AUTHOR]

The cancer atlas edited by several countries is the main resource for the analysis of the geographic variation of cancer risk. Correlating the observed spatial patterns with known or hypothesized risk factors is time‐consuming work for epidemiologists who need to deal with each cancer separately, breaking down the patterns according to sex and race. The recent literature has proposed to study more than one cancer simultaneously looking for common spatial risk factors. However, this previous work has two constraints: they consider only a very small (2–4) number of cancers previously known to share risk factors. In this article, we propose an exploratory method to search for latent spatial risk factors of a large number of supposedly unrelated cancers. The method is based on the singular value decomposition and nonnegative matrix factorization, it is computationally efficient, scaling easily with the number of regions and cancers. We carried out a simulation study to evaluate the method's performance and apply it to cancer atlas from the USA, England, France, Australia, Spain, and Brazil. We conclude that with very few latent maps, which can represent a reduction of up to 90% of atlas maps, most of the spatial variability is conserved. By concentrating on the epidemiological analysis of these few latent maps a substantial amount of work is saved and, at the same time, high‐level explanations affecting many cancers simultaneously can be reached. [ABSTRACT FROM AUTHOR]

AbstractNeural Bayes estimators are neural networks that approximate Bayes estimators in a fast and likelihood-free manner. Although they are appealing to use with spatial models, where estimation is often a computational bottleneck, neural Bayes estimators in spatial applications have, to date, been restricted to data collected over a regular grid. These estimators are also currently dependent on a prescribed set of spatial locations, which means that the neural network needs to be re-trained for new data sets; this renders them impractical in many applications and impedes their widespread adoption. In this work, we employ graph neural networks (GNNs) to tackle the important problem of parameter point estimation from data collected over arbitrary spatial locations. In addition to extending neural Bayes estimation to irregular spatial data, the use of GNNs leads to substantial computational benefits, since the estimator can be used with any configuration or number of locations and independent replicates, thus amortising the cost of training for a given spatial model. We also facilitate fast uncertainty quantification by training an accompanying neural Bayes estimator that approximates a set of marginal posterior quantiles. We illustrate our methodology on Gaussian and max-stable processes. Finally, we showcase our methodology on a data set of global sea-surface temperature, where we estimate the parameters of a Gaussian process model in 2161 spatial regions, each containing thousands of irregularly-spaced data points, in just a few minutes with a single graphics processing unit. [ABSTRACT FROM AUTHOR]

While log-Gaussian Cox process regression models are useful tools for modeling point patterns, they can be technically difficult to fit and require users to learn/adopt bespoke software. We show that, for suitably formatted data, we can actually fit these models using generalized additive model software, via a simple line of code, demonstrated on R by the popular mgcv package. We are able to do this because a common and computationally efficient way to fit a log-Gaussian Cox process model is to use a basis function expansion to approximate the Gaussian random field, as is provided by a generic bivariate smoother over geographic space. We further show that if basis functions are parameterized appropriately then we can estimate parameters in the spatial covariance function for the latent random field using a generalized additive model. We use simulation to show that this approach leads to model fits of comparable quality to state-of-the-art software, often more quickly. But we see the main advance from this work as lowering the technology barrier to spatial statistics for applied researchers, many of whom are already familiar with generalized additive model software. [ABSTRACT FROM AUTHOR]

The integration of multiple survey, administrative, and third-party data offers the opportunity to innovate and improve survey estimation via statistical modeling. With decreasing response rates and increasing interest for more timely and geographically detailed estimates, imputation methodology that combines multiple data sources to adjust for low unit response and allow for more detailed publication levels, including geographic estimates, is both timely and necessary. Motivated by the Advance Monthly Retail Trade Survey (MARTS) and Monthly Retail Trade Survey (MRTS), we propose Bayesian hierarchical multiple imputation-dependent data models with the goals of automating imputation for the MARTS by using historic MRTS data and providing geographically granular (state-level) estimates for the MRTS via mass imputation using third-party data and spatial dependence. As a natural byproduct of this approach, measures of uncertainty are provided. This article illustrates the advantages of applying established Bayesian hierarchical modeling techniques with multiple source data to address practical problems in official statistics and is, therefore, of independent interest. The motivating empirical studies are unified by their hierarchical modeling framework, which ultimately results in a more principled approach for estimation for the MARTS and a more geographically granular data product for the MRTS. [ABSTRACT FROM AUTHOR]

We introduce two algorithms for generating from the bimodal generalized von Mises-Fisher distribution on the sphere. This generalization of the von Mises-Fisher distribution is more flexible, in particular by allowing for multimodality, and it preserves many of the theoretical properties of the von Mises-Fisher. The first proposed generation algorithm is obtained from conditional simulation and acceptance-rejection. The second one is the Metropolis-Hastings with mixture of von Mises-Fisher as jumping or instrumental distribution. These two algorithms are compared through density estimations of generated polar angles. [ABSTRACT FROM AUTHOR]

We develop hierarchical models and methods in a fully parametric approach to generalized linear mixed models for any patterned covariance matrix. The Laplace approximation is used to marginally estimate covariance parameters by integrating over all fixed and latent random effects. The Laplace approximation relies on Newton–Raphson updates, which also leads to predictions for the latent random effects. We develop methodology for complete marginal inference, from estimating covariance parameters and fixed effects to making predictions for unobserved data. The marginal likelihood is developed for six distributions that are often used for binary, count, and positive continuous data, and our framework is easily extended to other distributions. We compare our methods to fully Bayesian methods, automatic differentiation, and integrated nested Laplace approximations (INLA) for bias, mean‐squared (prediction) error, and interval coverage, and all methods yield very similar results. However, our methods are much faster than Bayesian methods, and more general than INLA. Examples with binary and proportional data, count data, and positive‐continuous data are used to illustrate all six distributions with a variety of patterned covariance structures that include spatial models (both geostatistical and areal models), time series models, and mixtures with typical random intercepts based on grouping. [ABSTRACT FROM AUTHOR]

The global response to the COVID-19 pandemic between January 2020 and late 2021 saw extraordinary measures such as lockdowns and other restrictions being placed on citizens’ movements in many of the world’s major cities. In many of these cities, lockdowns required citizens to stay at home; non-essential business premises were closed, and movement was severely restricted. In this paper, we investigate the effect of these lockdowns and other pandemic response measures on crime counts within the local authorities of England and Wales. Using openly accessible crime records from major police forces in the UK from 2015 to 2023, we discuss the impacts of lockdowns on the incidences of crime. We show that as time passed and citizens’ response to the imposed measures eased, most types of crime gradually returned to pre-pandemic norms whilst others remained below their pre-pandemic levels. Furthermore, our work shows that the effects of pandemic response measures were not uniform across local authorities. We also discuss how the findings of this study contribute to law enforcement initiatives. [ABSTRACT FROM AUTHOR]

As India strives for development and economic growth inclusively among all segments of society, a detailed examination of disparities in access to basic amenities is essential to address social, economic, and environmental challenges that hinder the development process. This study aims to identify and categorize areas in India that lack household amenities. The conditions i) households without access to drinking water, ii) households without toilets, iii) households without electricity, iv) households without drainage, v) kachha type households, and vi) households classified as the poorest in the NFHS 2019–2021 data are examined. The spatial clustering of the chosen conditions is confirmed through Global Moran’s I. Getis-Ord Gi⋆ hotspot analysis is used to detect local spatial clustering. Further, the frequency of hot spots is calculated in each district and classified according to the level of deprivation. The district-wise analysis reveals that India’s northeast and the east are hotspots for deprivation. Based on an examination of India’s states and union territories, Jharkhand ranks the most deprived, followed by West Bengal, Bihar, Odisha, Chhattisgarh, and Meghalaya. The result also shows regional variations in deprivation across different states of India which can be attributed to reasons such as state government plans. Identifying these disparities can guide policymakers to enhance living standards and the overall well-being of the country. This study could help allocate resources more effectively and target the most deprived sections of society. [ABSTRACT FROM AUTHOR]

Biomass energy is one of the renewable energy sources used as an alternative to supply the increasing energy consumption in today's conditions. Appropriate determination of the locations of biomass power plant (BPP), which are considered to be of critical importance in energy efficiency, is necessary to obtain maximum benefit from renewable energy. In this study, it is aimed to perform spatial statistical analyzes by taking into account the location of BPPs, established in Turkey, and the attribute values in the location. Basic information was obtained by applying exploratory spatial data analysis and spatial pattern analysis. Spatial autocorrelation analyzes and spatial interpolation were performed by including the installed power values of BPP spatial point data as feature data. It was concluded in the spatial statistical analyzes obtained with ArcGIS Pro, which is used as a GIS software program, that the spatial distribution of BPPs according to their location and installed power values is not random. It has been shown as a result of the Kriging analysis applied for spatial interpolation that the power value predictions can be made according to the location of the newly installed BPPs by creating a forecasting map.

AbstractLatent Gaussian process (GP) models are flexible probabilistic nonparametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, that is, on large datasets. In this article, we present iterative methods to overcome this drawback. Among other things, we introduce and analyze several preconditioners, derive new convergence results, and propose novel methods for accurately approximating predictive variances. We analyze our proposed methods theoretically and in experiments with simulated and real-world data. In particular, we obtain a speed-up of an order of magnitude compared to Cholesky-based calculations and a 3-fold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite dataset. All methods are implemented in a free C++ software library with high-level Python and R packages. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee et al. (Stat Comput 31(4):51, 2021. https://doi.org/10.1007/s11222-021-10025-7) recently demonstrated that improved inference for areal unit count data can be achieved by carrying out modifications to a graph representing spatial correlations; specifically, they delete edges of the planar graph derived from border-sharing between geographic regions in order to maximise a specific objective function. In this paper, we address the computational complexity of the associated graph optimisation problem. We demonstrate that this optimisation problem is NP-hard; we further show intractability for two simpler variants of the problem. We follow these results with two parameterised algorithms that exactly solve the problem. The first is parameterised by both treewidth and maximum degree, while the second is parameterised by the maximum number of edges that can be removed and is also restricted to settings where the input graph has maximum degree three. Both of these algorithms solve not only the decision problem, but also enumerate all solutions with polynomial time precalculation, delay, and postcalculation time in respective restricted settings. For this problem, efficient enumeration allows the uncertainty in the spatial correlation to be utilised in the modelling. The first enumeration algorithm utilises dynamic programming on a tree decomposition of the input graph, and has polynomial time precalculation and linear delay if both the treewidth and maximum degree are bounded. The second algorithm is restricted to problem instances with maximum degree three, as may arise from triangulations of planar surfaces, but can output all solutions with FPT precalculation time and linear delay when the maximum number of edges that can be removed is taken as the parameter. [ABSTRACT FROM AUTHOR]

Research on spatial statistical methods related to population estimation at the building scale and its implications for urban land use has attained little attention. The main target of this study is to propose a new method for population estimation at the building level with minimal data and methodology and a high accuracy rate. In addition to this, it discusses urban population from various perspectives by using spatial statistical methods (Local Moran's I and Hot–Cold Spot) to examine the population calculated based on the number of residential units in buildings and the household size of the neighborhood along with urban land use types in the case of Bursa. The results showed the following: (1) The suggested method achieves a 76% accuracy rate in population estimation at the building level; (2) 64.6% of the city's population (2,101,581 individuals) is located in areas classified as Discontinuous High-Density Urban Fabric (50–80%) and Continuous Urban Fabric (>80); (3) 13.2% of the population is located in hot spot areas of these two types, while 14.5% is in cold spot areas. This research provides decision-makers with a framework for addressing urban problems related to housing, transportation, health, and energy in addition to the methods it proposes. [ABSTRACT FROM AUTHOR]

Policymakers need to develop measures to counter overcrowding and relocate excess tourism in congested areas to others with fewer visitors. This article proposes a methodological framework consisting of a survey and statistical tools to a gain deeper understanding of tourist profiles and characteristics and determine how covariates affect the ratio of each group in the market. Spatial analysis is performed to determine regional cluster patterns and propose measures aimed at alleviating congested areas by redirecting tourism to other destinations with less pressure without losing the economic impact of tourism. The proposed methodology is applied to international tourists in Spain and reveals some relevant aspects of four international tourism profiles. The analysis confirms the existence of spatial dependence between Spanish regions, suggesting that the application of public policies in one region could have implications for neighbouring ones. [ABSTRACT FROM AUTHOR]

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Health surveys allow exploring health indicators that are of great value from a public health point of view and that cannot normally be studied from regular health registries. These indicators are usually coded as ordinal variables and may depend on covariates associated with individuals. In this article, we propose a Bayesian individual‐level model for small‐area estimation of survey‐based health indicators. A categorical likelihood is used at the first level of the model hierarchy to describe the ordinal data, and spatial dependence among small areas is taken into account by using a conditional autoregressive distribution. Post‐stratification of the results of the proposed individual‐level model allows extrapolating the results to any administrative areal division, even for small areas. We apply this methodology to describe the geographical distribution of a self‐perceived health indicator from the Health Survey of the Region of Valencia (Spain) for the year 2016. [ABSTRACT FROM AUTHOR]

AbstractLow-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this article, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

The impact of sporting events on local economies and their spatial distribution is a topic of active policy debate. This study adds to the discussion by examining granular cellphone location data to assess the spillover effects of Major League Baseball (MLB) games in a major US city. Focusing on the 2019 season, we explore granular geospatial patterns in mobility and consumer spending on game days versus non-game days in the Saint Louis region. Through density-based clustering and hotspot analysis, we uncover distinct spatiotemporal signatures and variations in visitor affluence across different teams. This study uses features like game day characteristics, location data (latitude and longitude), business types, and spending data. A significant finding is that specific spatial clusters of economic activity are formed around the stadium, particularly on game days, with multiple clusters identified. These clusters reveal a marked increase in spending at businesses such as restaurants, bars, and liquor stores, with revenue surges of up to 38% in certain areas. We identified a significant change in spending patterns in the local economy during games, with results varying greatly across teams. Notably, the XGBoost model performs best, achieving a test R2 of 0.80. The framework presented enhances the literature at the intersection of urban economics, sports analytics, and spatial modeling while providing data-driven actionable insights for businesses and policymakers. [ABSTRACT FROM AUTHOR]

Research on social housing stigma has proliferated due to growing concern over the effects of territorial stigmatization. The stereotyping of social housing as a site of ill‐health, criminality, and low human capital stems from empirically ambiguous narratives created and recirculated through popular modes (e.g., social media platforms, news coverage). This paper combines principal component analysis, k‐means cluster analysis, and geographic information systems to create and visualize clusters denoting different levels of health, crime, human capital, and dwelling composition in the city of Toronto, Canada. The quantitative research design allows for the identification of "asymmetries," which are census tracts or neighbourhoods assigned to clusters indicative of high social housing density, and one of either sound health, low crime, or high human capital. The results reveal a spatial patterning of asymmetries in the inner city West End and Downtown, and in inner suburban North York, Etobicoke, and Scarborough. Overall, the paper illustrates the need to assess the empirical foundations of social housing stereotypes. Critically assessing stereotypes is important as they belie the rationale for social housing residents' living situations; pathologizes their identity, behaviour, and home; and generates public support for neoliberal solutions that displace long‐term residents from their communities. Key messages: Asymmetries are primarily located in the inner suburbs, and to a lesser degree in the inner city, exhibiting the suburbanization and spatial fix of stigma.Asymmetries are located in neighbourhoods at varying stages of gentrification, highlighting the lack of an empirical basis for redevelopment legitimated by stigma.Spatial statistics and GIS are viable territorial destigmatization tools. [ABSTRACT FROM AUTHOR]

We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not guaranteed to be positive definite on such domains, while existing non-Euclidean approaches fail to respect the partially Euclidean nature of these domains where the geodesic distance agrees with the Euclidean distances for some pairs of points. Using a visibility graph on the domain, we propose a class of covariance functions that preserve Euclidean-based covariances between points that are connected in the domain while incorporating the non-convex geometry of the domain via conditional independence relationships. We show that the proposed method preserves the partially Euclidean nature of the intrinsic geometry on the domain while maintaining validity (positive definiteness) and marginal stationarity of the covariance function over the entire parameter space, properties which are not always fulfilled by existing approaches to construct covariance functions on non-convex domains. We provide useful approximations to improve computational efficiency, resulting in a scalable algorithm. We compare the performance of our method with those of competing state-of-the-art methods using simulation studies on synthetic non-convex domains. The method is applied to data regarding acidity levels in the Chesapeake Bay, showing its potential for ecological monitoring in real-world spatial applications on irregular domains. [ABSTRACT FROM AUTHOR]

The scientific field of precision agriculture employs increasingly innovative techniques to optimize inputs, maximize profitability, and reduce environmental impact. However, obtaining a high number of soil samples is challenging in order to make precision agriculture viable. There is a trade-off between the amount of data needed and the time and resources spent to obtain these data compared to the accuracy of the maps produced with more or fewer points. In the present study, the research was based on an exhaustive dataset of apparent electrical conductivity (aEC) containing 3906 points distributed along 26 transects with spacing between each of up to 40 m, measured by the proximal soil sensor EM38-MK2, for a grain-producing area of 72 ha in São Paulo, Brazil. A second sparse dataset was simulated, showing only four transects with a 400 m distance and, in the end, only 162 aEC points. The aEC map via ordinary kriging (OK) from the grid with 26 transects was considered the reference, and two other mapping approaches were used to map aEC via sparse grid: kriging with external drift (KED) and geographically weighted regression (GWR). These last two methods allow the increment of auxiliary variables, such as those obtained by remote sensors that present spatial resolution compatible with the pivot scale, such as data from the Landsat-8, Aster, and Sentinel-2 satellites, as well as ten terrain covariates derived from the Alos Palsar digital elevation model. The KED method, when used with the sparse dataset, showed a relatively good fit to the aEC data (R2 = 0.78), with moderate prediction accuracy (MAE = 1.26, RMSE = 1.62) and reasonable predictability (RPD = 1.76), outperforming the GWR method, which had the weakest performance (R2 = 0.57, MAE = 1.78, RMSE = 2.30, RPD = 0.81). The reference aEC map using the exhaustive dataset and OK showed the highest accuracy with an R2 of 0.97, no systematic bias (ME = 0), and excellent precision (RMSE = 0.56, RPD = 5.86). Management zones (MZs) derived from these maps were validated using soil texture data from clay samples measured at 0–10 cm depth in a grid of 72 points. The KED method demonstrated the highest potential for accurately defining MZs for irrigation, producing a map that closely resembled the reference MZ map, thereby providing reliable guidance for irrigation management. [ABSTRACT FROM AUTHOR]

Land Surface Temperature (LST) is a vital satellite remote sensing-driven indicator of earth heat studies. LST can provide information about urban heat emission, urban climate, and human activities in urban areas. In recent years, the calculated LST for a satellite image pixel has been studied as a parameter affected by urban environment factors such as available land cover types in the same pixel. However, in this study, a scenario in which the calculated LST for a pixel is not only affected by the factors in the same pixel but also by the factors in the neighbor pixels is studied. Firstly, required maps for the calculated LST and influential factors (indicators of vegetation, building, and water surfaces) are produced from satellite remote sensing images. Secondly, the relationship between the LST and influential factors is modeled using the Ordinary Least Squares (OLS) model. Thirdly, Moran's I and Lagrange Multiplier tests are used to analyze the existence of spatial dependency and correlation in residuals of the OLS model. Fourthly, three spatial regression models (Spatially Lagged X (SLX), Spatial Lag (SL), and Spatial Error (SE) models) are used to model the spatial dependency and correlation between the LST and influential factors. Finally, the outcomes of the models are compared and evaluated. Results present related maps for the variables besides maps for spatial residuals in the spatial regression models. The outcomes of the models are investigated by p-values, log-likelihood, and RMSE. To conclude, the spatial regression models fitted the relation between the dependent and independent variables better than the OLS model. [ABSTRACT FROM AUTHOR]

We introduce a clustering method for time series based on tail dependence. Such a method also considers spatial constraints by means of a suitable procedure merging temporal and spatial dependence via extreme-value copulas. The cluster composition depends on the choice of the hyper-parameter α ∈ (0 , 1) used to calibrate the contribution of the spatial dependence to the overall dissimilarity. A novel heuristic approach to select α based on a suitable connectedness index associated to each cluster of the partition is proposed. [ABSTRACT FROM AUTHOR]

Spatio-ecological heterogeneity has a significant impact on various ecosystem properties, such as biodiversity patterns, variability in ecosystem resources, and species distributions. Given this perspective, remote sensing has gained widespread recognition as a powerful tool for assessing the spatial heterogeneity of ecosystems by analyzing the variability among different pixel values in both space and, potentially, time. Several measures of spatial heterogeneity have been proposed, broadly categorized into abundance-related measures (e.g., Shannon's H) and dispersion-related measures (e.g., Variance). A measure that integrates both abundance and distance information is the Rao's quadratic entropy (Rao's Q index), mainly used in ecology to measure plant diversity based on in-situ based functional traits. The question arises as to why one should use a complex measure that considers multiple dimensions and couples abundance and distance measurements instead of relying solely on simple dispersion-based measures of heterogeneity. This paper sheds light on the spatial version of the Rao's Q index, based on moving windows for its calculation, with a particular emphasis on its mathematical and statistical properties. The main objective is to theoretically demonstrate the strength of Rao's Q index in measuring heterogeneity, taking into account all its potential facets and applications, including (i) integrating multivariate data, (ii) applying differential weighting to pixels, and (iii) considering differential weighting of distances among pixel reflectance values in spectral space. [ABSTRACT FROM AUTHOR]

Despite the presence of a theoretical model describing the settlement patterns of Palaeolithic sites in Northwestern Iberia, it has not yet been empirically tested using statistical analysis. This study explores the settlement patterns of the Palaeolithic period in Northwestern Iberia within two regions that share similar chronology and research traditions: the Northern and Central Mountain ranges of Northwestern Iberia. Employing Geographic Information Systems (GIS) and spatial statistics, the methodology has provided robust empirical support for several aspects of the theoretical model. The study rigorously tested the theoretical model proposed in the existing literature using statistical analysis and a comprehensive dataset of 50 variables. The findings highlight significant regional distinctions in the settlement patterns of Palaeolithic sites within both areas of Northwestern Iberia. This research not only confirms certain hypotheses related to Palaeolithic site locations but also underscores the need for further examination and refinement of others, particularly considering the notable regional variations. [ABSTRACT FROM AUTHOR]

We introduce a model that can be used for the description of the distribution of species when there is scarcity of data, based on our previous work (Ballesteros et al. J Math Biol 85(4):31, 2022). We address challenges in modeling species that are seldom observed in nature, for example species included in The International Union for Conservation of Nature’s Red List of Threatened Species (IUCN 2023). We introduce a general method and test it using a case study of a near threatened species of amphibians called Plectrohyla Guatemalensis (see IUCN 2023) in a region of the UNESCO natural reserve “Tacaná Volcano”, in the border between Mexico and Guatemala. Since threatened species are difficult to find in nature, collected data can be extremely reduced. This produces a mathematical problem in the sense that the usual modeling in terms of Markov random fields representing individuals associated to locations in a grid generates artificial clusters around the observations, which are unreasonable. We propose a different approach in which our random variables describe yearly averages of expectation values of the number of individuals instead of individuals (and they take values on a compact interval). Our approach takes advantage of intuitive insights from environmental properties: in nature individuals are attracted or repulsed by specific features (Ballesteros et al. J Math Biol 85(4):31, 2022). Drawing inspiration from quantum mechanics, we incorporate quantum Hamiltonians into classical statistical mechanics (i.e. Gibbs measures or Markov random fields). The equilibrium between spreading and attractive/repulsive forces governs the behavior of the species, expressed through a global control problem involving an energy operator. [ABSTRACT FROM AUTHOR]

ABSTRACTThe health and societal impacts of COVID-19 have created tremendous interest in the scientific community, resulting in interdisciplinary research teams that combine their expertise to provide new insights into the epidemic. However, spatial computation, exploratory data analysis, and spatial data exploration tools have yet to be integrated into these dashboards. We present a Spatial Online Analytical Platform that integrates spatial analysis tools that enable users to explore and learn more about spatial patterns of COVID-19. We present three interaction classes to support users needs. Our first class allows users to apply user-defined data classifications and custom map color choices. The second class applies a risk index across the time series, informing users of the recent temporal trends. The third class allows users to hypothesize about the presence of spatial clusters and receive results on demand. Our SOLAP platform supports the data analysis and exploration needs of big spatial-temporal data.

As a strong human disturbance, coal mining has affected the ecosystem service function and economic value on mining area. However, there is a lack on the comparing for the long-term spatial scale evolution of landscape ecological risk after mining development based on different landforms in the same climate environment. Therefore, the spatial and temporal evolution characteristics of landscape ecological risk were explored on loess hilly and sandy land in the Yushenfu Mining Area based on the Landsat data from 1995—2021 with the construction of landscape ecological risk index and spatial statistical analysis methods. The results showed that: ① There was no significant changing between loess hilly and sandy land for the ecological risk pattern from 1995 to 2000. From 2000 to 2010, the low level ecological risk area changed to a higher level in the loess hilly region. In 2010, the proportion of medium-high, medium and medium-low ecological risk areas was 70% in the loess hilly area, while the high ecological risk area in the sand-covered area increased but not significant, and it was still dominated by medium-low ecological risk and account for 31%. Since 2010, the landscape ecological pattern tended to homogenization, and the landscape ecological risk gradually stabilized to a low-medium, medium and high-medium on loess hilly area, and the proportion of these three risk levels was 74% in 2021. The sandy landscape also formed a low, medium and low-medium ecological risk, and the proportion of the three risk levels was 77%, and decreased and stabilized gradually. ② From 1995 to 2021, the landscape ecological risks showed obvious spatially clustered distribution characteristics, and presented a clear hotspots and coldspots in Yushenfu Mining Area. The ecological risk hotspots were mainly located in the loess hilly area in the northeast and southeast of the study area where coal has been developed for a long time and the geological environment has been seriously damaged, and the ecological risk coldspots were mainly located in the sand-covered areas in the central part of study area which are still under resource exploration and survey. ③ Human disturbance was the most important factor affecting the landscape ecological risk in Yushenfu Mining Area, the determining force of q values in the loess area and the sand-covered area were 0.49−0.72 and 0.38−0.55, respectively, followed by vegetation coverage and temperature in the loess hilly area, and vegetation coverage and air temperature had a similar effects on landscape ecological risk in the sand-covered area, and the least factor was elevation for ecological risk on both landforms, the q values were less than 0.10. ④ The results of spatial and temporal landscape ecological risk indicated that the landscape pattern should be optimized according to the characteristics of different landforms in the process of ecological restoration in Yushenfu Mining Area, and the mining scheme should be optimized to reduce the surface ecological damage and the active restoration strategy should be actively carried out in the loess hilly area. Whilethe natural restorationcan be implemented to ensure the ecological stability on the sand-covered mining area.

Wildfires have become increasingly prevalent in the western United States, posing threats to human communities and the built environment. This study builds upon previous research by investigating the factors influencing wildfire hot spot distribution in Washington State. Using spatial regression models (generalized linear regression and geographically weighted regression), we examine the relationships between wildfire hot spots and various geographic features, including climate variables, human-caused ignitions, land use, population density, road density, and the wildland-urban interface. Our results indicate that lightning-caused fires and road density are significant factors contributing to hot spot intensity in central Washington, while human-caused ignitions play a crucial role in eastern Washington. Surprisingly, precipitation shows varied correlations with hot spots, with some areas experiencing an unexpected positive relationship between precipitation and hot spot intensity due to increased fuel growth. The study highlights the importance of localized approaches to wildfire mitigation, emphasizing the need for tailored risk reduction strategies based on regional factors.

Background: Fatal opioid-involved overdose rates increased precipitously from 5.0 per 100,000 population to 33.5 in Massachusetts between 1999 and 2022. Methods: We used spatial rate smoothing techniques to identify persistent opioid overdose-involved fatality clusters at the ZIP Code Tabulation Area (ZCTA) level. Rate smoothing techniques were employed to identify locations of high fatal opioid overdose rates where population counts were low. In Massachusetts, this included areas with both sparse data and low population density. We used Local Indicators of Spatial Association (LISA) cluster analyses with the raw incidence rates, and the Empirical Bayes smoothed rates to identify clusters from 2011 to 2021. We also estimated Empirical Bayes LISA cluster estimates to identify clusters during the same period. We constructed measures of the socio-built environment and potentially inappropriate prescribing using principal components analysis. The resulting measures were used as covariates in Conditional Autoregressive Bayesian models that acknowledge spatial autocorrelation to predict both, if a ZCTA was part of an opioid-involved cluster for fatal overdose rates, as well as the number of times that it was part of a cluster of high incidence rates. Results: LISA clusters for smoothed data were able to identify whether a ZCTA was part of a opioid involved fatality incidence cluster earlier in the study period, when compared to LISA clusters based on raw rates. PCA helped in identifying unique socio-environmental factors, such as minoritized populations and poverty, potentially inappropriate prescribing, access to amenities, and rurality by combining socioeconomic, built environment and prescription variables that were highly correlated with each other. In all models except for those that used raw rates to estimate whether a ZCTA was part of a high fatality cluster, opioid overdose fatality clusters in Massachusetts had high percentages of Black and Hispanic residents, and households experiencing poverty. The models that were fitted on Empirical Bayes LISA identified this phenomenon earlier in the study period than the raw rate LISA. However, all the models identified minoritized populations and poverty as significant factors in predicting the persistence of a ZCTA being part of a high opioid overdose cluster during this time period. Conclusion: Conducting spatially robust analyses may help inform policies to identify community-level risks for opioid-involved overdose deaths sooner than depending on raw incidence rates alone. The results can help inform policy makers and planners about locations of persistent risk. [ABSTRACT FROM AUTHOR]

In this research, the spatial correlation between the variables representing Bouguer gravity anomaly and seismicity in Iran is evaluated. For this purpose, the gravity anomalies and seismicity data of this region have been analyzed statistically as well as geostatistically, for the period 1975-2021. Based on the findings of this study, it can be concluded that the significant correlation observed between the variables of gravity anomaly variations and the seismicity-related variables, especially the variables related to the frequency of earthquake occurrences, suggests that the gravity anomaly variations can be considered as an affective factor in seismic activity of this region. The Iranian Plateau is one of the most seismically active regions on the Earth because of its geologic and tectonic setting. This plateau is marked by high topography relief and also by great changes in gravitational and isostatic anomalies across it. Many researchers have studied the variations of gravitational anomalies across Iran, and some have pointed to the relationships between these anomalies and seismicity in this region. The Bouguer gravity anomaly is obtained by making the necessary corrections to measurements taken directly from the ground stations, and well reflects the deep density variations in the crust. This anomaly can also clearly show changes in crustal thickness in different regions, such that areas with high crustal thicknesses show negative anomalies and areas with low crustal thicknesses show positive anomalies. In this study, at first, the study region was divided into rectangles with dimensions of 0.5 by 0.5 geographical degrees and then the variables related to the seismicity and gravity anomalies were calculated and computed for each cell. Pearson correlation coefficients between these variables were computed and validated using statistical software Minitab (ver. 16.2.2). Also, maps representing the spatial distribution pattern of these variables were prepared. The remarkable similarity between the spatial patterns of variations of these variables indicates a strong correlation between the Bouguer gravity anomaly and seismicity in this region. The Pearson correlation coefficient values calculated between the variables also confirm this correlation. These values indicate that both variables of average Bouguer anomaly and the range of variations of this anomaly show a significant positive correlation with the seismicity-related variables. This degree of correlation is stronger for the variable of the Bouguer anomaly variation and moreover, this variable is more correlated with the seismicity variables associated with the frequency of earthquakes. In the next step, variograms were prepared. The results obtained show that among the seismicity-related variables of the region, the b seismicity parameter (from the Gutenberg-Richter relation) has more spatial variability and show high spatial autocorrelation up to long distances. On the other hand, the other variables related to earthquake frequency and magnitude of earthquakes show less spatial autocorrelation. The variograms provided for the two variables representing the bouguer anomaly also show remarkable similarity to the seismicityrelated diagrams. This similarity is more pronounced for the variable of the Bouguer anomaly variation. The remarkable similarities of the variograms, along with the similarities of the spatial distribution maps of these variables, may indicate a close relationship between these two series of variables. Finally, it can be concluded that gravitational forces, especially forces caused by isostatic imbalances, can play an important role in the process of earthquake occurrences in Iran. [ABSTRACT FROM AUTHOR]

The objective of the study was to analyze the occurrence of forest fires in a conservation unit (CU) of the Brazilian savannah using remote sensing techniques and statistical methods developed for spatial punctual processes. To conduct the spatial analysis of fires, fire polygons mapped using Landsat 8 satellite images were used. The fires were considered into size classes to better illustrate the spatial patterns. The analysis of the spatial distribution of fires utilized Ripley's K-function, in addition to the Kcross function to verify spatial interaction. The results show that the year 2015 had the highest number of fires and burned area. Smaller fires represent a greater number of occurrences, located mostly on CU boundaries. The spatial distribution of forest fires is not random and can cluster on a scale of approximately 6 km. There is a strong spatial interaction between forest fires and traditional communities, particularly with fires smaller than 100 hectares. However, these communities are not responsible for large fires. These results contribute to better-targeted forest fire prevention and combat policies, serving as management tools for the protected area. [ABSTRACT FROM AUTHOR]

Simple Summary: Targeted therapies can induce strong tumor regression, but they typically fail to eradicate metastatic cancers. The elucidation of the causes that enable cancers to survive within a residual disease is essential for finding eradication strategies. The ability of cancers to survive eradication reflects not only cell-intrinsic sensitivities, but also microenvironmental effects. Paracrine signals produced by fibroblast, non-neoplastic cells that make tumor stroma, can provide strong but spatially limited therapy protection. Even though this phenomenon is well-established, its contribution to the ability of tumors to escape eradication remains poorly understood. To address this gap of knowledge, we developed an in silico model that recapitulates the effect of stroma on therapy responses in tumor tissues. This model enabled us to evaluate the contribution of spatial aspects of stroma-mediated resistance. Our analyses reveal that stroma dispersal might be the most important yet overlooked aspect of stromal resistance that determines the overall tumor responses to therapy. The response of tumors to anti-cancer therapies is defined not only by cell-intrinsic therapy sensitivities but also by local interactions with the tumor microenvironment. Fibroblasts that make tumor stroma have been shown to produce paracrine factors that can strongly reduce the sensitivity of tumor cells to many types of targeted therapies. Moreover, a high stroma/tumor ratio is generally associated with poor survival and reduced therapy responses. However, in contrast to advanced knowledge of the molecular mechanisms responsible for stroma-mediated resistance, its effect on the ability of tumors to escape therapeutic eradication remains poorly understood. To a large extent, this gap of knowledge reflects the challenge of accounting for the spatial aspects of microenvironmental resistance, especially over longer time frames. To address this problem, we integrated spatial inferences of proliferation-death dynamics from an experimental animal model of targeted therapy responses with spatial mathematical modeling. With this approach, we dissected the impact of tumor/stroma distribution, magnitude and distance of stromal effects. While all of the tested parameters affected the ability of tumor cells to resist elimination, spatial patterns of stroma distribution within tumor tissue had a particularly strong impact. [ABSTRACT FROM AUTHOR]

This article introduces bayesian spatial smoothing models for disease mapping—a specific application of small area estimation where the full universe of data is known—to a wider audience of public health professionals using firearm suicide as a motivating example. Besag, York, and Mollié (BYM) Poisson spatial and space–time smoothing models were fitted to firearm suicide counts for the years 2014-2018. County raw death rates in 2018 ranged from 0 to 24.81 deaths per 10 000 people. However, the highest mortality rate was highly unstable, based on only 2 deaths in a population of approximately 800, and 80.5% of contiguous US counties experienced fewer than 10 firearm suicide deaths and were thus suppressed. Spatially smoothed county firearm suicide mortality estimates ranged from 0.06 to 4.05 deaths per 10 000 people and could be reported for all counties. The space–time smoothing model produced similar estimates with narrower credible intervals as it allowed counties to gain precision from adjacent neighbors and their own counts in adjacent years. bayesian spatial smoothing methods are a useful tool for evaluating spatial health disparities in small geographies where small numbers can result in highly variable rate estimates, and new estimation techniques in R software have made fitting these models more accessible to researchers. [ABSTRACT FROM AUTHOR]

Geostatistical prediction methods are increasingly used in earth sciences and engineering to improve upon our knowledge of attributes in space and time. During mining activities, it is very important to have an estimate of any contamination of the soil and groundwater in the area for environmental reasons and to guide the reclamation once mining operations are finished. In this paper, we present the geostatistical analysis of the water content in certain pollutants (Cd and Mn) in a group of mines in Northern Greece. The monitoring points that were studied are 62. The aim of this work is to create a contamination prediction map that better represents the values of Cd and Mn, which is challenging based on the small sample size. The correlation between Cd and Mn concentration in the groundwater is investigated during the preliminary analysis of the data. The logarithm of the data values was used, and after removing a linear trend, the variogram parameters were estimated. In order to create the necessary maps of contamination, we employed the method of ordinary Kriging (OK) and inversed the transformations using bias correction to adjust the results for the inverse transform. Cross-validation shows promising results ( ρ = 65 % for Cd and ρ = 52 % for Mn, RMSE = 25.9 ppb for Cd and RMSE = 25.1 ppm for Mn). As part of this work, the Spartan Variogram model was compared with the other models and was found to perform better for the data of Mn. [ABSTRACT FROM AUTHOR]

Background Distributed lag non-linear models (DLNMs) are the reference framework for modelling lagged non-linear associations. They are usually used in large-scale multi-location studies. Attempts to study these associations in small areas either did not include the lagged non-linear effects, did not allow for geographically-varying risks or downscaled risks from larger spatial units through socioeconomic and physical meta-predictors when the estimation of the risks was not feasible due to low statistical power. Methods Here we proposed spatial Bayesian DLNMs (SB-DLNMs) as a new framework for the estimation of reliable small-area lagged non-linear associations, and demonstrated the methodology for the case study of the temperature-mortality relationship in the 73 neighbourhoods of the city of Barcelona. We generalized location-independent DLNMs to the Bayesian framework (B-DLNMs), and extended them to SB-DLNMs by incorporating spatial models in a single-stage approach that accounts for the spatial dependence between risks. Results The results of the case study highlighted the benefits of incorporating the spatial component for small-area analysis. Estimates obtained from independent B-DLNMs were unstable and unreliable, particularly in neighbourhoods with very low numbers of deaths. SB-DLNMs addressed these instabilities by incorporating spatial dependencies, resulting in more plausible and coherent estimates and revealing hidden spatial patterns. In addition, the Bayesian framework enriches the range of estimates and tests that can be used in both large- and small-area studies. Conclusions SB-DLNMs account for spatial structures in the risk associations across small areas. By modelling spatial differences, SB-DLNMs facilitate the direct estimation of non-linear exposure-response lagged associations at the small-area level, even in areas with as few as 19 deaths. The manuscript includes an illustrative code to reproduce the results, and to facilitate the implementation of other case studies by other researchers. [ABSTRACT FROM AUTHOR]

When analyzing spatially referenced event data, the criteria for declaring rates as "reliable" is still a matter of dispute. What these varying criteria have in common, however, is that they are rarely satisfied for crude estimates in small area analysis settings, prompting the use of spatial models to improve reliability. While reasonable, recent work has quantified the extent to which popular models from the spatial statistics literature can overwhelm the information contained in the data, leading to oversmoothing. Here, we begin by providing a definition for a "reliable" estimate for event rates that can be used for crude and model-based estimates and allows for discrete and continuous statements of reliability. We then construct a spatial Bayesian framework that allows users to infuse prior information into their models to improve reliability while also guarding against oversmoothing. We apply our approach to county-level birth data from Pennsylvania, highlighting the effect of oversmoothing in spatial models and how our approach can allow users to better focus their attention to areas where sufficient data exists to drive inferential decisions. We then conclude with a brief discussion of how this definition of reliability can be used in the design of small area studies. [ABSTRACT FROM AUTHOR]

Motivated by the general ability of cross-validation to reduce overfitting and mean square error, we develop a cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross-validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach, which may be used to model different distributional characteristics, exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Having indicated that our new framework generalizes many existing statistical approaches, we then establish different theoretical properties for it, including large sample properties. We further recognize that nonparametric intensity estimation is an instance of Papangelou conditional intensity estimation, which we exploit to apply our new statistical theory to kernel intensity estimation. Using independent thinning-based cross-validation, we numerically show that the new approach substantially outperforms the state-of-the-art in bandwidth selection. Finally, we carry out intensity estimation for a dataset in forestry and a dataset in neurology. [ABSTRACT FROM AUTHOR]

In countries where population census data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model‐based geostatistical methods leverage covariate information and spatial smoothing to reduce the variability of estimates but often ignore the survey design, while traditional small area estimation approaches may not incorporate both unit‐level covariate information and spatial smoothing in a design consistent way. We propose a smoothed model‐assisted estimator that accounts for survey design and leverages both unit‐level covariates and spatial smoothing. Under certain regularity assumptions, this estimator is both design consistent and model consistent. We compare it with existing design‐based and model‐based estimators using real and simulated data. [ABSTRACT FROM AUTHOR]