log-gaussian cox process

Bayesian modeling of large-scale spatiotemporal count data is hindered by the non-conjugacy between standard log-Gaussian process priors and Poisson likelihoods, leading to inefficient variational inference or MCMC. Method: We propose an Auto-Regressive Gamma Process (ARGP)-based fully conjugate framework that induces a temporally stationary and spatially sparse spatiotemporal structure, ensuring exact conjugacy between the latent process prior and Poisson observations. This enables efficient Gibbs sampling with linear computational complexity. By decomposing Poisson latent variables and modeling them via ARGP, the approach achieves both interpretability and scalability. Results: Experiments on synthetic and real-world datasets demonstrate substantial improvements in parameter estimation accuracy, posterior convergence speed, and out-of-sample predictive performance—particularly for generalization to novel spatiotemporal locations.

This paper addresses nonparametric estimation of the intensity function of spatial point processes. We propose a novel random forest–based method that unifies treatment of both covariate-free and covariate-inclusive settings: in the absence of covariates, it naturally accommodates irregular spatial domains and low-dimensional manifolds without boundary correction; with covariates, it efficiently handles high-dimensional features and supports out-of-bag cross-validation and quantitative variable importance assessment. Theoretically, we establish consistency and derive convergence rates for the estimator. Empirically, the method achieves accuracy comparable to state-of-the-art approaches and significantly outperforms them when covariate information is rich. Our core innovation lies in deeply integrating the adaptive nonlinear modeling capacity of random forests with the intrinsic structure of spatial point processes—thereby overcoming traditional kernel-based methods’ reliance on domain regularity and explicit boundary correction, and substantially broadening the applicability and practical utility of nonparametric spatial intensity estimation.

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.

To address the challenge of jointly detecting spatiotemporal change points and identifying spatial clusters in large-scale spatiotemporal count data, this paper proposes a doubly fused penalized Poisson regression model—the first to achieve simultaneous and consistent estimation of temporal breakpoints and spatially abrupt clusters. Methodologically, we design a dual structured penalty that jointly enforces temporal jumps and spatial proximity, and develop an iterative soft-thresholding optimization algorithm. Theoretically, we establish an asymptotic statistical inference framework and rigorously prove consistency and asymptotic normality of the estimators. Extensive simulations and real-world applications—including disease outbreak monitoring and urban anomaly detection—demonstrate that our method significantly outperforms existing approaches in localization accuracy and cluster identification precision, while exhibiting strong robustness and linear scalability with respect to sample size.

To address computational bottlenecks in latent spatial field inference and pointwise prediction in geostatistical models, this paper proposes Bayesian Predictive Stacking (BPS). BPS analytically aggregates posterior distributions of regression coefficients and spatial processes across multiple hyperparameter configurations, circumventing iterative algorithms such as MCMC and enabling fully parallelized inference. Its key innovation lies in a unified stacking framework that jointly combines predictive means and posterior densities, underpinned by infill asymptotic theory that guarantees statistical consistency. Experiments demonstrate that BPS achieves predictive accuracy comparable to full-sample Bayesian inference while drastically reducing computational time. The method is thus highly efficient, robust to hyperparameter specification, and scalable to large spatial datasets.

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.

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.

This study addresses the challenges of high-dimensional parameter estimation and the difficulty of specifying broad prior ranges in inhomogeneous bivariate log-Gaussian Cox processes when covariates are present. To overcome these issues, the authors propose a two-stage decoupled estimation framework: first, classical Poisson regression is employed to estimate first-order intensity parameters; subsequently, simulation-based inference combined with deep neural networks is used to learn latent field parameters. Innovatively, spatial point patterns are transformed into two-dimensional image inputs, enabling the network to directly capture complex spatial structures. This approach effectively circumvents the traditional reliance of simulation-based inference on expansive parameter spaces, achieving high-precision latent field estimation in simulation studies and demonstrating practical utility through application to gorilla distribution data.

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.

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.