double zero-inflated spatio-temporal modeling

This paper addresses the recovery of conditional distribution functions for continuous variables under threshold-classified observations—particularly when the distribution frequently attains boundary values (0 or 1) and exhibits spatiotemporal dependence and covariate effects, rendering standard binomial models inadequate. We propose a boundary-inflated binomial mixture model that jointly incorporates a Dirac measure (to capture point mass at boundaries) and a binomial kernel (to model interior continuity), embedded within a dynamic Gaussian process to account for spatiotemporal dependence. A Bayesian inference framework is developed using Pólya–Gamma data augmentation, enabling efficient and robust distributional regression. Simulation studies demonstrate that our method significantly improves distributional fit and predictive stability near boundaries compared to conventional binomial regression. The approach holds substantial practical value for ecological and environmental applications involving threshold-based measurements.

To address pervasive truncation and missing observations in spatiotemporal regional data, this paper proposes a unified Bayesian spatiotemporal modeling framework. The method innovatively integrates spatial autoregressive (SAR) and directed acyclic graph autoregressive (DAGAR) structures within a Gaussian Markov random field (GMRF) formulation, augmented with a temporal autoregressive (AR) component to enable interpretable joint modeling. Unlike conventional conditional autoregressive (CAR) models, the DAGAR-AR framework flexibly captures asymmetric and heterogeneous spatial dependencies. Its Bayesian inferential paradigm naturally supports uncertainty quantification and simultaneous estimation of missing values. In simulation studies and an empirical application to Beijing CO concentration data, the proposed approach significantly outperforms baseline methods—including limit-of-detection (LOD) substitution and mean imputation—achieving superior predictive accuracy and enhanced structural interpretability.

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.

To address computational challenges in modeling non-Gaussian spatiotemporal data—specifically, the intractability of analytically integrating random effects and weak parameter identifiability impeding MCMC convergence—this paper proposes a Bayesian inference framework based on predictive stacking. Innovatively integrating generalized conjugate multivariate distribution theory with an extended Diaconis–Ylvisaker conjugate prior family, the method enables exact sampling from conditional posteriors and facilitates Bayesian model integration across disparate model configurations. It circumvents the computational bottlenecks inherent in conventional generalized linear mixed models, where closed-form integration of random effects is infeasible. Simulation studies demonstrate substantially improved MCMC convergence speed and parameter estimation accuracy relative to standard MCMC approaches. The framework is further validated on large-scale spatiotemporal count data from the North American Breeding Bird Survey, confirming its robustness and scalability.

In spatial regression, spatial confounding arises when spatial covariates correlate with high-frequency components of the latent spatial random effect, biasing coefficient estimates. Conventional two-stage frequentist approaches (e.g., spatial+) fail to propagate uncertainty from the first stage and cannot guarantee orthogonality between covariate residuals and the spatial effect in the high-frequency domain. This paper proposes the first Bayesian joint modeling framework that end-to-end integrates spatial covariate adjustment with spatial effect estimation. We introduce a novel joint prior on smoothing parameters that explicitly decouples high-frequency collinearity, balancing deconfounding and predictive accuracy. Built upon a hierarchical Gaussian random field and inference via Integrated Nested Laplace Approximation (INLA), our method demonstrates, in simulations and real-data applications, substantially reduced coefficient bias, improved nominal coverage of posterior credible intervals, and more robust, interpretable statistical inference.

This study addresses the challenges posed by potentially infinite-dimensional covariates and non-mixing dependence structures in spatiotemporal data by proposing a nonparametric regression framework conditioned on second-order stationary covariates. The work innovatively replaces conventional mixing assumptions with a polynomially decaying moment contraction (PMC) condition, enabling effective modeling of infinite-dimensional spatiotemporal covariates. Employing kernel estimation techniques, the authors establish statistical consistency of the mean function estimator under the PMC condition and construct simultaneous confidence intervals based on a central limit theorem. Comprehensive theoretical analysis, simulation studies, and applications to two real-world datasets demonstrate that the proposed method exhibits strong finite-sample performance and is suitable for hypothesis testing regarding the functional form of the mean.

Environmental exposure assessment is often hindered by substantial uncertainty arising from spatiotemporal misalignment and high missingness across heterogeneous data sources (e.g., satellite and ground-based observations). To address this, we propose a Bayesian weighted regression framework with an embedded spatiotemporal kernel that directly models irregularly spaced spatiotemporal observations—bypassing preprocessing steps such as imputation or forced alignment. Our method innovatively integrates Voronoi spatial integration with irregular temporal increment approximation, thereby avoiding bias inherent in conventional two-stage modeling while principledly capturing spatial and temporal lag effects. Evaluated on PM₂.₅ estimation across California, the framework achieves over 50% higher R² than state-of-the-art models and markedly reduces prediction uncertainty, yielding robust, high-resolution spatiotemporal exposure surfaces. The framework is naturally extensible to multivariate settings and supports general kernel specifications, establishing a novel paradigm for environmental exposure modeling under complex observational constraints.

Bayesian Gaussian process (GP) modeling for large-scale, highly censored spatial data faces prohibitive computational costs and struggles to capture spatial nonstationarity. Method: We propose an efficient Bayesian inference framework integrating Vecchia approximation with spatially varying coefficient models (SVCMs). This is the first systematic application of Vecchia approximation to SVCMs under substantial censoring, reducing GP complexity from O(n³) to O(nm²) (m ≪ n) while preserving spatial heterogeneity. Full Bayesian inference is performed via MCMC, and results are benchmarked against geographically weighted regression (GWR). Results: On the Toulouse soil contamination dataset—with 67% censoring—the method robustly estimates spatially varying coefficients, delivering high interpretability and competitive predictive accuracy. It substantially enhances scalability and practical applicability of Bayesian spatial models in real-world, complex scenarios.

This work addresses the challenge of conducting calibrated Bayesian inference for parametric models whose likelihood functions are intractable, numerically unstable, or computationally prohibitive. Existing approaches lack finite-sample calibration guarantees under such conditions. The authors propose a fully probabilistic inference framework that requires neither a prior nor a likelihood, relying solely on the model’s simulation capability. By leveraging permutation-invariant functions—such as depth functions—to rank parameters and introducing a closed-form rescaling procedure, the method achieves finite-sample frequentist calibration. To the best of the authors’ knowledge, this is the first approach to provide theoretical calibration guarantees in a setting devoid of both likelihood and prior specifications. Empirical evaluations across four benchmark tasks—including differential privacy and the Ising model—as well as a spatial analysis of the 2025 U.S. measles outbreak demonstrate the method’s strong practical utility and robustness.

This study addresses the challenge of distinguishing between true zero precipitation and unobserved rainfall below the detection limit in daily precipitation records, which both manifest as zeros in the data. The authors propose the first Bayesian hierarchical spatiotemporal model that jointly represents these two types of zeros alongside positive precipitation amounts. The framework combines a probit regression to model the probability of precipitation occurrence, a gamma regression for precipitation intensities exceeding the detection threshold, and a threshold-censoring mechanism integrated with Gaussian processes to capture spatial dependence. Applied to 15 years of springtime daily precipitation data from the Ebro River basin in Spain, the model reveals that the detection threshold substantially influences precipitation frequency and upper quantiles in wetter regions, though its effect on total precipitation volume remains limited.