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We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As for the Matérn case, this class allows for a continuous parameterization of smoothness of the underlying Gaussian random field, being additionally compactly supported. The paper is divided into three parts: first, we characterize the equivalence of two Gaussian measures with GW covariance function, and we provide sufficient conditions for the equivalence of two Gaussian measures with Matérn and GW covariance functions. In the second part, we establish strong consistency and asymptotic distribution of the maximum likelihood estimator of the microergodic parameter associated to GW covariance model, under fixed domain asymptotics. The third part elucidates the consequences of our results in terms of (misspecified) best linear unbiased predictor, under fixed domain asymptotics. Our findings are illustrated through a simulation study: the former compares the finite sample behavior of the maximum likelihood estimation of the microergodic parameter with the given asymptotic distribution. The latter compares the finite-sample behavior of the prediction and its associated mean square error when using two equivalent Gaussian measures with Matérn and GW covariance models, using covariance tapering as benchmark.

Recent coordinated efforts, in which numerous general circulation climate models have been run for a common set of experiments, have produced large datasets of projections of future climate for various scenarios. Those multimodel ensembles sample initial conditions, parameters, and structural uncertainties in the model design, and they have prompted a variety of approaches to quantifying uncertainty in future climate change. International climate change assessments also rely heavily on these models. These assessments often provide equal-weighted averages as best-guess results, assuming that individual model biases will at least partly cancel and that a model average prediction is more likely to be correct than a prediction from a single model based on the result that a multimodel average of present-day climate generally outperforms any individual model. This study outlines the motivation for using multimodel ensembles and discusses various challenges in interpreting them. Among these challenges are that the number of models in these ensembles is usually small, their distribution in the model or parameter space is unclear, and that extreme behavior is often not sampled. Model skill in simulating present-day climate conditions is shown to relate only weakly to the magnitude of predicted change. It is thus unclear by how much the confidence in future projections should increase based on improvements in simulating present-day conditions, a reduction of intermodel spread, or a larger number of models. Averaging model output may further lead to a loss of signal—for example, for precipitation change where the predicted changes are spatially heterogeneous, such that the true expected change is very likely to be larger than suggested by a model average. Last, there is little agreement on metrics to separate \"good\" and \"bad\" models, and there is concern that model development, evaluation, and posterior weighting or ranking are all using the same datasets. While the multimodel average appears to still be useful in some situations, these results show that more quantitative methods to evaluate model performance are critical to maximize the value of climate change projections from global models.

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the “big data” era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics.

The last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides an overview of statistical modeling techniques for space–time processes, where space is the sphere representing our planet. In particular, we make a distintion between (a) second order-based approaches and (b) practical approaches to modeling temporally evolving global processes. The former approaches are based on the specification of a class of space–time covariance functions, with space being the two-dimensional sphere. The latter are based on explicit description of the dynamics of the space–time process, that is, by specifying its evolution as a function of its past history with added spatially dependent noise. We focus primarily on approach (a), for which the literature has been sparse. We provide new models of space–time covariance functions for random fields defined on spheres cross time. Practical approaches (b) are also discussed, with special emphasis on models built directly on the sphere, without projecting spherical coordinates onto the plane. We present a case study focused on the analysis of air pollution from the 2015 wildfires in Equatorial Asia, an event that was classified as the year’s worst environmental disaster. The paper finishes with a list of the main theoretical and applied research problems in the area, where we expect the statistical community to engage over the next decade.

We discuss the experiences and results of the AppStatUZH team’s participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different subcompetitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.

Additive Bayesian networks (ABNs) provide a flexible framework for modeling complex multivariate dependencies among variables of different distributions, including Gaussian, Poisson, binomial, and multinomial. This versatility makes ABNs particularly attractive in clinical research, where heterogeneous data are frequently collected across distinct groups. However, standard applications either pool all data together, ignoring group-specific variability, or estimate separate models for each group, which may suffer from limited sample sizes. In this work, we extend ABNs to a mixed-effect framework that accounts for group structure through partial pooling, and we evaluate its performance in a large-scale simulation study. We compare three strategies—partial pooling, complete pooling, and no pooling—cross a wide range of network sizes, sparsity levels, group configurations, and sample sizes. Performance is assessed in terms of structural accuracy, parameter estimation accuracy, and predictive performance. Our results demonstrate that partial pooling consistently yields superior structural and parametric accuracy while maintaining robust predictive performance across all evaluated settings for grouped data structures. These findings highlight the potential of mixed-effect ABNs as a versatile approach for learning probabilistic graphical models from grouped data with diverse distributions in real-world applications.

Stochastically generated streamflow time series are widely used in water resource planning and management. Such series represent sets of plausible yet unobserved streamflow realizations which should reproduce the main characteristics of observed data. These characteristics include the distribution of daily streamflow values and their temporal correlation as expressed by short- and long-range dependence. Existing streamflow generation approaches have mainly focused on the time domain, even though simulation in the frequency domain provides good properties. These properties comprise the simulation of both short- and long-range dependence as well as extension to multiple sites. Simulation in the frequency domain is based on the randomization of the phases of the Fourier transformation. We here combine phase randomization simulation with a flexible, four-parameter kappa distribution, which allows for the extrapolation to as yet unobserved low and high flows. The simulation approach consists of seven steps: (1) fitting the theoretical kappa distribution, (2) normalization and deseasonalization of the marginal distribution, (3) Fourier transformation, (4) random phase generation, (5) inverse Fourier transformation, (6) back transformation, and (7) simulation. The simulation approach is applicable to both individual and multiple sites. It was applied to and validated on a set of four catchments in Switzerland. Our results show that the stochastic streamflow generator based on phase randomization produces realistic streamflow time series with respect to distributional properties and temporal correlation. However, cross-correlation among sites was in some cases found to be underestimated. The approach can be recommended as a flexible tool for various applications such as the dimensioning of reservoirs or the assessment of drought persistence. Highlights. Stochastic simulation of streamflow time series for individual and multiple sites by combining phase randomization and the kappa distribution. Simulated time series reproduce temporal correlation, seasonal distributions, and extremes of observed time series. Simulation procedure suitable for use in water resource planning and management.

Interpolation of a spatially correlated random process is used in many scientific areas. The best unbiased linear predictor, often called a kriging predictor in geostatistical science, requires the solution of a (possibly large) linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. Monte Carlo simulations support the theoretical results. An application to a large climatological precipitation dataset is presented as a concrete and practical illustration.

Several key processes in freshwater ecology are governed by the connectivity inherent to dendritic river networks. These have extensively been analyzed from a geomorphological and hydrological viewpoint, yet structures classically used in ecological modeling have been poorly representative of the structure of real river basins, often failing to capture well‐known scaling features of natural rivers. Pioneering work identified optimal channel networks (OCNs) as spanning trees reproducing all scaling features characteristic of natural stream networks worldwide. While OCNs have been used to create landscapes for studies on metapopulations, biodiversity, and epidemiology, their generation has not been generally accessible. Given the increasing interest in dendritic riverine networks by ecologists and evolutionary biologists, we here present a method to generate OCNs and, to facilitate its application, we provide the R‐package OCNet. Owing to the stochastic process generating OCNs, multiple network replicas spanning the same surface can be built; this allows performing computational experiments whose results are irrespective of the particular shape of a single river network. The OCN construct also enables the generation of elevational gradients derived from the optimal network configuration, which can constitute three‐dimensional landscapes for spatial studies in both terrestrial and freshwater realms. Moreover, the package provides functions that aggregate OCNs into an arbitrary number of nodes, calculate several descriptors of river networks, and draw relevant network features. We describe the main functionalities of the package and its integration with other R‐packages commonly used in spatial ecology. Moreover, we exemplify the generation of OCNs and discuss an application to a metapopulation model for an invasive riverine species. In conclusion, OCNet provides a powerful tool to generate realistic river network analogues for various applications. It thereby allows the design of spatially realistic studies in increasingly impacted ecosystems and enhances our knowledge on spatial processes in freshwater ecology in general. Recently, research on spatial dynamics in ecology and evolution has bloomed. However, spatial structures used in theoretical and empirical ecological studies are often not representative of realistic landscapes. This is particularly true for river networks, which are of paramount interest to ecologists owing to their wide (but currently severely declining) biodiversity. Indeed, most of ecological work has been neglecting the scaling character of real river networks, despite well‐established knowledge in the fields of geomorphology and hydrology. Here, we present a method to create optimal channel networks (OCNs, i.e., river network analogues reproducing all topographic and scaling features of natural rivers), and the respective R‐package allowing their generation and analysis. We review the theoretical background underlying the OCN concept, present the main package functionalities, discuss possible applications in the realm of ecology and evolution, and detail how the package can be integrated with other popular R‐packages in spatial ecology.

Background Cystic and alveolar echinococcosis (CE and AE) are neglected tropical diseases caused by Echinococcus granulosus sensu lato and E. multilocularis, and are emerging zoonoses in Kyrgyzstan. In this country, the spatial distribution of CE and AE surgical incidence in 2014-2016 showed marked heterogeneity across communities, suggesting the presence of ecological determinants underlying CE and AE distributions. Methodology/Principal findings For this reason, in this study we assessed potential associations between community-level confirmed primary CE (no.=2359) or AE (no.=546) cases in 2014-2016 in Kyrgyzstan and environmental and climatic variables derived from satellite-remote sensing datasets using conditional autoregressive models. We also mapped CE and AE relative risk. The number of AE cases was negatively associated with 10-year lag mean annual temperature. Although this time lag should not be considered as an exact measurement but with associated uncertainty, it is consistent with the estimated 10-15-year latency following AE infection. No associations were detected for CE. We also identified several communities at risk for CE or AE where no disease cases were reported in the study period. Conclusions/Significance Our findings support the hypothesis that CE is linked to an anthropogenic cycle and is less affected by environmental risk factors compared to AE, which is believed to result from spillover from a wild life cycle. As CE was not affected by factors we investigated, hence control should not have a geographical focus. In contrast, AE risk areas identified in this study without reported AE cases should be targeted for active disease surveillance in humans. This active surveillance would confirm or exclude AE transmission which might not be reported with the present passive surveillance system. These areas should also be targeted for ecological investigations in the animal hosts.