locally stationary spatio-temporal modeling

To address computational bottlenecks and high-dimensional parameter inference in modeling nonstationary spatial processes, this paper proposes a scalable full Bayesian framework. First, it introduces an analytically tractable representation based on spatially varying covariance kernels to explicitly capture local dependence structures. Second, it designs a nested alternating hybrid Hamiltonian Monte Carlo (HMC) algorithm to enable efficient and stable posterior sampling at large spatial scales. Third, it integrates formal model selection with parameter identifiability analysis to ensure inferential reliability. The framework demonstrates parameter identifiability and posterior consistency on synthetic data. On real-world applications—NDVI remote sensing and soil lead contamination datasets—it achieves significant improvements in predictive accuracy and uncertainty quantification quality. By unifying theoretical rigor with computational scalability, the approach establishes a new paradigm for modeling complex geospatial data.

This paper addresses the challenge of jointly modeling spatially shared variation and localized temporal dynamics in areal spatiotemporal data. We propose a hierarchical Bayesian model grounded in spatially correlated Gaussian processes. Innovatively, we model time-varying parameters as a stochastic process with a conditional autoregressive (CAR) prior and explicitly incorporate dependence between temporal variability and temporal range, enabling more flexible and interpretable characterization of spatiotemporal evolution. Spatial information is propagated through shared variance components, allowing the model to capture cross-regional common patterns while preserving region-specific temporal trajectories. Bayesian inference is performed via a MALA–MH–Gibbs hybrid MCMC algorithm. Evaluated on real-world datasets—malaria incidence in Mozambique and food insecurity prevalence in Cameroon—the model achieves significantly higher predictive accuracy than conventional approaches, demonstrating clear utility for public health surveillance and policy decision-making.

Traditional models struggle to characterize nonstationary spatial point processes—e.g., those exhibiting intensity discontinuities, hotspots, or spatial heterogeneity. To address this, we propose a Cox process model based on stochastic spatial partitioning. Our method employs a partitioned Gaussian process prior to explicitly capture intensity discontinuities and local variations; integrates a random segmentation mechanism with infinite-dimensional MCMC sampling to avoid grid-based discretization, thereby preserving nonparametric flexibility while substantially reducing computational cost; and incorporates spatial covariates to elucidate underlying drivers of intensity variation. Experiments on synthetic and real-world datasets demonstrate that the approach achieves high-fidelity inference of nonstationary intensity structures, robustly identifies change-point boundaries and hotspot regions, and provides a scalable, interpretable nonparametric Bayesian framework for complex spatial point patterns.

Traditional spatial modeling relies on stationarity and isotropy assumptions, which increasingly fail in real-world applications; meanwhile, existing nonstationary approaches often sacrifice either flexibility or computational efficiency. To address this, we propose a covariate-driven, modular covariance function—built upon the Matérn kernel—that enables parameterized, decoupled modeling of multiple sources of nonstationarity, including marginal standard deviation, geometric anisotropy, and smoothness. Our formulation ensures interpretability, computational scalability, and intuitive visualizability. By incorporating a covariate-adaptive construction mechanism and a large-scale adaptation algorithm, the method achieves superior predictive performance over state-of-the-art nonstationary models in both simulation studies and real-world analysis of Swiss precipitation data. It simultaneously attains high model fidelity and low computational overhead, demonstrating robust scalability to large spatial datasets.

Existing graph-based Gaussian processes lack effective kernel functions capable of modeling spatiotemporal coupling dynamics on graphs. Method: This paper introduces the first derivation framework for non-separable spatiotemporal graph kernels grounded in stochastic partial differential equations (SPDEs). By establishing an explicit connection between SPDEs and graph Gaussian processes—leveraging spectral graph theory—we derive two classes of non-separable kernels corresponding to the heat and wave equations, respectively, thereby overcoming the modeling limitations of conventional separable kernels in capturing spatiotemporal interactions. Contribution/Results: The proposed kernels significantly outperform state-of-the-art graph kernels on complex spatiotemporal graph tasks—including diffusion and oscillation processes—demonstrating superior expressive power and predictive accuracy in empirical evaluations. This work establishes a novel paradigm for spatiotemporal covariance modeling over graph-structured data.

Traditional geostatistical methods rely on second-order moments and Gaussian assumptions, which are inadequate for capturing non-Gaussian spatial dependence. This work addresses this limitation by leveraging Sklar’s theorem to introduce a copula-based framework that decouples marginal distributions from the spatial dependence structure. The authors systematically develop spatial copula models applicable at both fixed point sets and process levels, emphasizing Kolmogorov consistency to clarify distinctions between these two modeling paradigms. The framework is further extended to spatio-temporal settings and supports flexible marginal specifications. By integrating spatial statistics, copula theory, and stochastic processes, this study establishes a unified approach for modeling non-Gaussian spatial dependence, elucidating the relationships, strengths, and limitations of existing methodologies, thereby advancing both theoretical understanding and practical applications in the field.

This study addresses the limitation of conventional wind turbine power curve models, which typically neglect terrain effects and thus struggle to accurately represent wind energy production in complex terrains. To overcome this, the authors propose a nonparametric spatiotemporal Gaussian process model that systematically incorporates terrain covariates for the first time. The model introduces a shared set of representative temporal covariates to handle temporal misalignment across multiple turbines and employs a separable kernel structure to efficiently capture spatiotemporal dependencies while reducing computational complexity. Experimental results on real-world wind farm data demonstrate that the proposed approach significantly outperforms existing baselines, achieving higher prediction accuracy and enabling quantitative assessment of how distinct terrain features influence turbine performance.

This work addresses the limitations of traditional spatiotemporal modeling approaches, which rely on covariance structures that tightly couple spatial and temporal components, leading to high computational costs. The authors propose a coarse-to-fine spatiotemporal modeling framework (CF-STM) that, for the first time, decouples multiscale locally weighted spatial representations from local state-space temporal models, enabling efficient, covariance-free modeling. This decoupling allows flexible selection of temporal dynamics without altering the spatial structure, substantially enhancing model interpretability and computational efficiency. Empirical evaluations demonstrate that CF-STM achieves predictive accuracy comparable to existing scalable methods in Monte Carlo simulations while incurring lower computational overhead. Furthermore, when applied to Tokyo residential land price data, the framework effectively captures complex spatiotemporal evolution patterns.

Traditional spatial deformation methods struggle to model covariate-driven nonstationary spatial dependencies and exhibit limited generalization. This work proposes a covariate-driven diffeomorphic spatial deformation framework that represents the deformation as a function of covariates, generating smooth and invertible mappings via velocity fields in a Lie algebra. To enhance stability and generalizability, the method incorporates a physics-informed truncation strategy for high-order interaction terms. It is the first approach to enable nonstationary Gaussian process extrapolation under covariate conditioning, demonstrating superior small-sample predictive performance on both synthetic data and real-world applications in manufacturing and geostatistics.

Existing spatiotemporal modeling approaches struggle to flexibly capture arbitrary fractional smoothness under nonseparable covariance structures and lack computationally efficient frameworks. This work addresses these limitations by constructing a nonseparable model based on the diffusion-based Matérn covariance through a spatiotemporal fractional stochastic partial differential equation. By introducing a rational approximation for temporal discretization, the method yields a low-order vector autoregressive moving average (VARMA) process. It provides, for the first time, an efficient approximation of arbitrary fractional spatiotemporal smoothness, with rigorous pointwise convergence of the covariance function and explicit convergence rates. Numerical experiments demonstrate that even a low-order VARMA accurately approximates the true process, enables effective parameter recovery, and significantly improves predictive performance when temporal smoothness is correctly specified, as successfully illustrated in modeling daily mean temperatures over mainland France across three months.