<p>Modeling high-dimensional spatio-temporal count data remains challenging when the observations exhibit excess zeros, serial dependence, and spatially structured heterogeneity. To address this setting, we develop a hierarchical spatio-temporal mixed zero-inflated Poisson (Mixed ZIP) model that combines temporal and spatial lag effects with region-specific random effects. The random effects are assigned modified Conditional Autoregressive (CAR) priors, allowing neighborhood-based smoothing while accommodating local heterogeneity in the latent intensity process. Posterior computation for this model is nontrivial because the hierarchical structure couples zero inflation, autoregressive dynamics, and spatial dependence. We therefore propose a Laplace-informed Gibbs sampler, in which local Laplace approximations are used for parameter blocks without closed-form conditional updates, while conjugate components are updated by exact Gibbs steps and Metropolis–Hastings corrections are introduced where required. This strategy yields a computationally tractable inference scheme for high-dimensional settings while preserving Bayesian validity. Simulation studies indicate that the proposed method can recover the main model parameters with stable accuracy across different levels of spatial heterogeneity. We further apply the model to traffic-injury emergency call data from the Chengdu 120 Emergency Medical Command Center. The empirical results show that the proposed framework captures zero inflation, spatial dependence, and temporal dynamics in a coherent manner, and provides favorable performance in intensity estimation, sparsity representation, and residual dependence diagnostics relative to several benchmark models. These features make the proposed method valuable for differentiated EMS response strategies, optimization of emergency service zoning, and improved traffic-incident management.</p>

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A Bayesian zero-inflated poisson model with random effects for spatio-temporal emergency calls

  • Haoran Li,
  • Honglei Wei,
  • Zhou He,
  • Maowu Pu,
  • Haitao Zheng

摘要

Modeling high-dimensional spatio-temporal count data remains challenging when the observations exhibit excess zeros, serial dependence, and spatially structured heterogeneity. To address this setting, we develop a hierarchical spatio-temporal mixed zero-inflated Poisson (Mixed ZIP) model that combines temporal and spatial lag effects with region-specific random effects. The random effects are assigned modified Conditional Autoregressive (CAR) priors, allowing neighborhood-based smoothing while accommodating local heterogeneity in the latent intensity process. Posterior computation for this model is nontrivial because the hierarchical structure couples zero inflation, autoregressive dynamics, and spatial dependence. We therefore propose a Laplace-informed Gibbs sampler, in which local Laplace approximations are used for parameter blocks without closed-form conditional updates, while conjugate components are updated by exact Gibbs steps and Metropolis–Hastings corrections are introduced where required. This strategy yields a computationally tractable inference scheme for high-dimensional settings while preserving Bayesian validity. Simulation studies indicate that the proposed method can recover the main model parameters with stable accuracy across different levels of spatial heterogeneity. We further apply the model to traffic-injury emergency call data from the Chengdu 120 Emergency Medical Command Center. The empirical results show that the proposed framework captures zero inflation, spatial dependence, and temporal dynamics in a coherent manner, and provides favorable performance in intensity estimation, sparsity representation, and residual dependence diagnostics relative to several benchmark models. These features make the proposed method valuable for differentiated EMS response strategies, optimization of emergency service zoning, and improved traffic-incident management.