spatial point processes

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.

This work addresses the challenge of jointly modeling variable point counts and spatial configurations in spatial point process generation by proposing the Existence Field Diffusion Model (EFDM). EFDM introduces, for the first time, an existence field into a diffusion framework, assigning each latent point a continuous existence variable to unify the modeling of point cardinality and location without requiring explicit discrete dimensional jumps. By constructing a joint continuous diffusion mechanism over both existence variables and spatial coordinates, EFDM enables symmetric, flexible, and unified generation of variable-cardinality point processes. Experimental results demonstrate that the proposed model significantly improves generation quality and modeling capability across multiple variable-cardinality datasets.

Bayesian spatial point process (SPP) modeling faces challenges including heavy reliance on numerical integration, high computational cost, and labor-intensive hyperparameter tuning. To address these, we propose a multi-stage recursive Bayesian framework that integrates parallel computation with recursive posterior updating. This enables efficient estimation of model coefficients and derived parameters within compact observation windows, while supporting posterior predictive inference for total abundance and point locations in unobserved regions. Compared to conventional approaches, our method substantially reduces dependence on numerical integration and manual tuning, enhancing both computational efficiency and scalability. We validate the framework through simulation studies and application to remote-sensing data of harbor seals in Johns Hopkins Inlet, Glacier Bay, Alaska. Results demonstrate superior accuracy and robustness, particularly under sparse observational regimes. The proposed method provides a novel, scalable tool for spatially explicit population modeling and conservation decision-making in ecology.

In spatial point process modeling, geocoding-induced coordinate duplication—such as aggregation to centroid locations—violates the location-uniqueness assumption of models like the log-Gaussian Cox process (LGCP); conventional approaches (e.g., deduplication or jittering) introduce bias. This paper proposes a data-preserving modeling framework that explicitly accounts for duplicate points in second-order intensity estimation. Our key contribution is a modified minimum contrast estimation (MMC) method that incorporates the duplication structure directly into the second-order moment intensity function of the LGCP and its spatial statistical inference framework. Simulation studies demonstrate that MMC substantially outperforms existing heuristic methods in terms of accuracy and robustness. Applied to 2008–2009 Afghanistan conflict event data, the method yields more accurate and reliable estimates of clustering structure, validating its practical utility for real-world geocoded point patterns subject to aggregation artifacts.

Existing spatial spectral analysis methods are constrained by data types (e.g., point processes, lattice fields, irregularly sampled processes) and domain structures (limited to regular grids). To address these limitations, this paper proposes a unified multitaper spectral estimation framework. Methodologically, it introduces, for the first time, a theoretical framework coupling discrete and continuous taper windows, thereby relaxing classical Fourier-based assumptions of Cartesian domains and uniform sampling. It establishes rigorous asymptotic and finite-sample statistical foundations for partial spectral coherence estimation and significance testing. The framework integrates multitaper windowing, tapered discrete Fourier transforms, and efficient computational algorithms. Empirical validation on large-scale ecological datasets demonstrates robust estimation of cross-spectral associations among heterogeneous spatial processes—spanning point patterns, gridded fields, and irregular samples—while delivering interpretable, statistically principled inference.

This study addresses a key limitation of traditional marked point process models, which commonly assume independence between marks and locations—an assumption often violated in real-world applications such as forestry. To overcome this constraint, the authors propose a unified framework that, for the first time, enables comprehensive modeling, parameter estimation, simulation, and visualization of location-dependent marked point processes within the R programming environment. Grounded in spatial point process theory, the approach integrates statistical modeling with computational tools to support fitting to empirical data, model diagnostics, and generation of realistic spatial patterns. By relaxing the restrictive independence assumption, this work provides a practical and extensible analytical toolkit for researchers in ecology and related fields.

This study addresses the challenge that observed spatial point patterns are often degraded by missed detections (sparsity) and positional errors (displacement), which can severely bias inference. Focusing on Poisson point processes, the authors propose a unified framework that jointly estimates the underlying intensity function nonparametrically while simultaneously learning a parametric model for both the sparsity mechanism and the displacement scale. Under mild conditions, they rigorously establish model identifiability—a first for enabling joint nonparametric inference of the degradation mechanisms and the true intensity function. Simulations demonstrate that the proposed method substantially outperforms misspecified models that ignore such observational degradations. The approach is successfully applied to real-world data on North Atlantic right whale calls in Cape Cod Bay, showcasing its practical utility.

Gaussian processes face significant challenges in large-scale spatial prediction, including high computational costs, the trade-off between accuracy and efficiency in low-rank approximations, and sensitivity to contaminated data. This work proposes an ensemble approach based on partitioned predictive processes (PP), incorporating a multi-resolution overlapping partitioning strategy that effectively balances scalability and predictive accuracy under a fixed number of inducing points. Theoretical analysis establishes, for the first time, the asymptotic robustness of this PP framework. Empirical evaluations demonstrate that the proposed method substantially outperforms existing approaches in both synthetic and real-world large-scale geostatistical tasks, achieving superior efficiency, high prediction accuracy, and strong robustness against data contamination.

This study addresses the challenge of disentangling background spatial inhomogeneity—driven by site-specific attractiveness—from inter-individual repulsive interactions in pedestrian waiting behavior, using repeated observations of spatial point patterns. To this end, the authors propose a novel semi-parametric spatial point process model that integrates a determinantal point process with a Gibbs point process. For the first time, repeated spatial point patterns are incorporated into the inference framework of such models, enabling parameter estimation and model assessment based on multiple independent and identically distributed spatial realizations. Applied to real-world pedestrian waiting scenarios, the method successfully reproduces key empirical spatial characteristics, demonstrating its effectiveness in capturing complex crowd distributions and achieving a tight integration of methodological innovation with practical application.

This study addresses a key limitation in traditional spatial capture–recapture models, which assume that animal activity centers follow a Poisson process and thereby ignore spatial dependencies arising from social aggregation, territorial behavior, or unobserved habitat preferences, leading to inaccurate density estimates. To overcome this, the authors propose a novel framework based on penalized regression splines, employing Laplace-approximated penalized marginal maximum likelihood to fit a log-Gaussian Cox process. This approach flexibly captures nonlinear effects of covariates on animal density and, for the first time, integrates penalized splines with log-Gaussian Cox processes into spatial capture–recapture modeling, thereby relaxing the restrictive conditional independence assumption of Poisson processes. Simulations and two empirical case studies demonstrate that the method substantially improves the accuracy of spatial density estimation while maintaining robustness in total population abundance inference.