ABSTRACT Accurate spatial prediction on the sphere is fundamental for global environmental applications such as climate monitoring and oceanographic analysis. Existing approaches, however, often struggle to balance computational efficiency, predictive accuracy, and the ability to accommodate heterogeneous spatial structures. We propose a multi‐resolution spatial modeling framework that integrates thin‐plate spline (TPS) basis functions with Gaussian process modeling. The framework begins with a fixed‐effects representation based on a hierarchy of nearly orthogonal TPS basis functions ordered by smoothness, thereby providing a multi‐resolution decomposition of spatial variation. This allows large‐scale patterns to be captured efficiently while preserving interpretability. To represent localized dependencies, we extend the model with a random effect governed by a tapered Matérn covariance, which models fine‐scale structure while ensuring scalability through sparse matrix operations. Model complexity is adaptively controlled using the conditional Akaike information criterion (cAIC), which simultaneously selects the number of basis functions and determines the contribution of the Gaussian process component. Numerical experiments and a global sea surface temperature application show how our method balances predictive accuracy with computational feasibility, establishing its role as a powerful solution for large‐scale spatial modeling on the sphere.

ABSTRACT In geostatistical inference, preferential sampling takes place when the locations of point‐referenced data are related to the latent spatial process of interest. Traditional geostatistical models can lead to biased inferences and predictions under preferential sampling. We introduce an extended Bayesian hierarchical framework that models both the observed locations and the responses jointly, using a spatial point process for the locations and a geostatistical process for the responses. We illustrate extensions beyond the classical log‐Gaussian Cox process for the sampling locations, combined with a Gaussian process for the responses. We also introduce simpler methods for accounting for preferential sampling that are less computationally demanding at the expense of prediction accuracy. We validate our models through simulation, demonstrating their effectiveness in correcting biases and improving prediction accuracy. We apply our models to decadal average temperature data from the Global Historical Climate Network in the Southwestern United States and show that preferential sampling could be present in some spatial regions.

ABSTRACT Accurate high‐resolution spatial and temporal wind speed data is critical for estimating the wind energy potential of a location. For real‐time wind speed prediction, statistical models typically depend on high‐quality (near) real‐time data from official meteorological stations to improve forecasting accuracy. Personal weather stations (PWS) offer an additional source of real‐time data and broader spatial coverage than official stations. However, they are not subject to rigorous quality control and may exhibit bias or measurement errors. This article presents a framework for incorporating PWS data into statistical models for validated official meteorological station data via a two‐stage approach. First, bias correction is performed on PWS wind speed data using reanalysis data. Second, we implement a Bayesian hierarchical spatiotemporal model that accounts for varying measurement error in the PWS data. This enables wind speed prediction across a target area, and is particularly beneficial for improving predictions in regions sparse in official monitoring stations. Our results show that including bias‐corrected PWS data improves prediction accuracy compared with using meteorological station data alone, with a 5% reduction in prediction error on average across all sites. The results are comparable with popular reanalysis products, but unlike these numerical weather models our approach is available in real‐time and offers improved uncertainty quantification.

ABSTRACT Compound events (CEs), commonly defined as the “combination of multiple drivers and/or hazards that contributes to societal or environmental risk”, often result in amplified impacts compared to individual hazards. In order to estimate the return period of bivariate CEs, a novel nonparametric approach employing bivariate Generalized Pareto distributions (bi‐GPD) is proposed and compared to a copula‐based approach. Special attention is given to account for temporal dependencies and nonconcurrent compound events. The latter are defined as excess of variables over a threshold at a relatively close time. The return period of such bivariate events is carefully defined and closed‐form expressions are obtained for both approaches. Simulations reveal the bi‐GPD approach is effective in case of positive asymptotic dependence and should be avoided in case of asymptotic independence. The novel approach is then applied to ERA5 reanalysis data to analyze two types of compound events: a spatial CE with simultaneous floods due to accumulated precipitation across two large watersheds in France and a preconditioned CE consisting of a devastating flood triggered by extreme precipitation over a saturated soil.

ABSTRACTIn this study, we propose a new kernel prediction approach based on the Kibria‐Lukman methodology to reduce the effects of multicollinearity in partially linear mixed measurement error models. The performance of the proposed kernel Kibria‐Lukman estimator/predictor is evaluated and compared with several existing alternatives, including the kernel, kernel ridge, and kernel Liu estimators/predictors, using the matrix mean square error criterion. Furthermore, we examine the asymptotic normality of the proposed method and address the case of an unknown covariance matrix of measurement errors. To support the theoretical findings, both a real earthquake dataset and an extensive Monte Carlo simulation study are analyzed.

ABSTRACTThe block maxima approach, which consists of dividing a series of observations into equal‐sized blocks to extract the block maxima, is commonly used for identifying and modeling extreme events using the generalized extreme value (GEV) distribution. In the analysis of coastal wave surge levels, the underlying data that generate the block maxima typically have missing observations. Consequently, the observed block maxima may not correspond to the true block maxima, yielding biased estimates of the GEV distribution parameters. Various parametric modeling procedures are proposed to account for the presence of missing observations under a block maxima framework. The performance of these estimators is compared through an extensive simulation study and illustrated by an analysis of extreme wave surges in Atlantic Canada.

ABSTRACTSpectroscopy plays a crucial role in various scientific and industrial applications, enabling the analysis of complex materials and their interactions with incident radiation. Hyperspectral remote sensing, also known as imaging spectroscopy, is essential for numerous Earth science applications, spanning multiple disciplines, including ecology, geology, and cryosphere research. With the abundance of current orbital imaging spectrometers, and with space agencies and commercial companies set to expand their use in the next few years, developing methodologies that maximize the utility of these data is crucial. Identifying the wavelength ranges of diagnostic absorption features in spectra is essential for understanding the relationship between spectral data and responses of interest. In this paper, we propose a statistical approach that utilizes Functional Partial Least Squares (FPLS) to model the spectral data as smooth functions and study their impact on the response variable along sub‐intervals of the domain. To capture the localized relationships within specific sub‐intervals, termed impact ranges, we present a novel two‐stage estimation procedure to identify the midpoint and half‐length of the impact ranges. Additionally, we introduce an algorithm for iteratively applying the proposed two‐stage approach to estimate both the number and location of potential impact ranges. The proposed procedure is evaluated via Monte Carlo simulation and is applied to a real dataset of spectra to identify the location of the diagnostic absorption features for predicting calcium carbonate (CaCO3) content in soil. Our methodology accurately estimates the number and location of impact ranges, corresponding to absorption features in spectral data.

ABSTRACTThis study provides a comprehensive evaluation of the computational performance of R, MATLAB, Python, and Julia for spatial and spatio‐temporal modelling, focusing on high‐dimensional datasets typical in geospatial statistical analysis. We benchmark each language across key tasks, including matrix manipulations and transformations, iterative programming routines, and Input/Output processes, all of which are critical in environmetrics. The results demonstrate that MATLAB excels in matrix‐based computations, while Julia consistently delivers competitive performance across a wide range of tasks, establishing itself as a robust, open‐source alternative. Python, when combined with libraries like NumPy, shows strength in specific numerical operations, offering versatility for general‐purpose programming. R, despite its slower default performance in raw computations, proves to be highly adaptable; by linking to optimized libraries like OpenBLAS or MKL and integrating C++ with packages like Rcpp, R achieves significant performance gains, becoming competitive with the other languages. This study also provides practical guidance for researchers to optimize R for geospatial data processing, offering insights to support the selection of the most suitable language for specific modelling requirements.