Hsin-Cheng Huang

Constructs multi-resolution thin-plate spline basis functions on the sphere for use in spatial regression and large-scale spatial prediction problems. Implements the basis system described in Huang, Huang, and Ing (2025) "Multi-Resolution Spatial Methods on the Sphere: Efficient Prediction for Global Data", Environmetrics, . Heavy computations are written in 'C++' via 'Rcpp' with optional 'OpenMP' parallelism.

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.

The field of historical climate reconstruction through documentary evidences has made significant advances in recent years, including a global synthesis of the index approach in climate reconstruction (Nash et al., 2021), a global documentary climate dataset (Burgdorf et al., 2023), and new perspectives to study historical climatology (White et al., 2022). Based on the progress, this study addresses two specific research questions: 1) What are the numerical structures and characteristics of the reconstructed climate index data across existing datasets from various continents? (2) Are these structures and characteristics reflective of long-term climatological traits in the regions, or are they controlled by other factors? By answering the questions, we collected climate index data from Africa, Australia, China, Europe, India and South America to analyze the data structure in each dataset. Each dataset’s structure was then compared against modern observational data, including ERA5 and the Global Historical Climatology Network (GHCN) monthly data, to identify correlations and asses credibility of the climate index data. The analysis involves spatial and temporal comparisons, statistical tests, and discussions on data quality and limitations.

We investigate extremes of PM in Taiwan using data from Environmental Protection Administration monitoring stations. The objective is to examine long‐term trends in PM extremes and short‐term spikes, measured by daily 1‐hour maximums, as they relate to human exposure and acute health risks in daily life. To model daily 1‐hour maximum PM concentrations across space and time, we adopt the generalized extreme value (GEV) distribution. Extending beyond location‐specific temporal extreme‐value models, we develop a spatio‐temporal varying‐coefficient GEV framework in which the distributional parameters evolve smoothly over space and time through spatio‐temporal basis functions. This formulation leverages information from neighboring sites and adjacent times, enabling the model to capture both broad‐scale structures and localized variability in extremes. The framework yields marginal distributions of extreme PM at any location and time, accounting for spatial heterogeneity, seasonal dynamics, and irregular data availability. The method is computationally efficient and can be implemented with existing R packages. Application to Taiwanese air‐quality data reveals a general decline in extreme PM events over the past decade, though substantial regional variability persists across Taiwan.

International Press of Boston - publishers of scholarly mathematical and scientific journals and books

In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic that tracks a stable microergodic parameter of the exponential covariance function, allowing us to address the intricate challenges of nonstationary processes that lack repeated measurements. We implement the fused lasso technique to elucidate nonstationary patterns at various resolutions. For prediction purposes, we segment the spatial domain into stationary sub-regions via Voronoi tessellations. Additionally, we devise a robust test for stationarity based on contrasting the sample means of our proposed statistics between two selected Voronoi subregions. The effectiveness of our method is demonstrated through simulation studies and its application to a precipitation dataset in Colorado.

The Taiwan air quality monitoring network (TAQMN) and the AirBox network both monitor PM2.5 in Taiwan. The TAQMN, managed by Taiwan's Environmental Protection Administration (EPA), provides high-quality PM2.5 measurements at 77 monitoring stations. The AirBox network launched more recently consists of low-cost, small internet-of-things (IoT) microsensors (i.e., AirBoxes) at thousands of locations. While the AirBox network provides broad spatial coverage, its measurements are unreliable and require calibrations. However, applying a universal calibration procedure to all AirBoxes does not work well because the calibration line varies with local factors, including the chemical compositions of PM2.5, which are not homogeneous in space. Therefore, different calibrations are needed at different locations to adapt to their local environments. Unfortunately, AirBoxes and EPA locations are misaligned, challenging the calibration task. In this paper, we propose a spatial model with spatially varying coefficients to account for the heterogeneity in the data. Our method gives spatially adaptive calibrations of AirBoxes and produces accurate PM2.5 concentration estimates with their error bars at any location, incorporating two types of measurements. In addition, the proposed method is robust to outliers, requires no colocated data, and provides calibration formulas for new AirBoxes once they are added to the network. We illustrate our approach using hourly PM2.5 data in 2020. After the calibration, the results show that the PM2.5 prediction improves by about 38%–68% in root-mean-squared prediction error. Once the calibration formulas are established, we can obtain reliable PM2.5 values even if we ignore EPA data.