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<p>Modeling spatial count data can be challenging when it exhibits complicated geographic relationships, non-linear trends, or asymmetrical dispersion. To address these issues, we present a versatile Bayesian framework that combines a count model with semi-parametric regression and is based on renewal theory. Our method uses Integrated Nested Laplace Approximation (INLA) and provides coherent posterior uncertainty (credible and predictive intervals) along with fast and accurate results. We evaluate our model using three real-world scenarios. Initially, we employ the dataset of Mackerel egg counts, a benchmark in spatial statistics, to validate the reliability of our model. Subsequently, we examine a novel dataset concerning lung and bronchus cancer mortality in Iowa, correlating environmental variables such as ozone, PM2.5, and green space with health outcomes. We analyze precipitation patterns in Alberta, Canada, utilizing May 2024 data on days with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ge 1\)</EquationSource> </InlineEquation> mm of rainfall to forecast absent places, essential for climate planning. Our strategy tackles three core difficulties in spatial count data: (i) dispersion that can be either above or below Poisson via a renewal-based Gamma–Count likelihood, (ii) non-linear covariate effects via Bayesian smoothers, and (iii) spatial correlation over irregular domains via thin-plate spline (TPS) fields. Across three datasets, this specification yields improved predictive fit and better-calibrated uncertainty than Poisson and negative-binomial baselines. This reasonable, comprehensible instrument enables researchers in public health, environmental science, and risk assessment to provide insights that foster healthier communities and a more resilient world.</p>

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Bayesian semi-parametric spatial modeling of dispersed count data with INLA: applications in public health and climate risk

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Mahsa Nadifar,
  • Andriette Bekker,
  • Mohammad Arashi,
  • Abel Ramoelo

摘要

Modeling spatial count data can be challenging when it exhibits complicated geographic relationships, non-linear trends, or asymmetrical dispersion. To address these issues, we present a versatile Bayesian framework that combines a count model with semi-parametric regression and is based on renewal theory. Our method uses Integrated Nested Laplace Approximation (INLA) and provides coherent posterior uncertainty (credible and predictive intervals) along with fast and accurate results. We evaluate our model using three real-world scenarios. Initially, we employ the dataset of Mackerel egg counts, a benchmark in spatial statistics, to validate the reliability of our model. Subsequently, we examine a novel dataset concerning lung and bronchus cancer mortality in Iowa, correlating environmental variables such as ozone, PM2.5, and green space with health outcomes. We analyze precipitation patterns in Alberta, Canada, utilizing May 2024 data on days with \(\ge 1\) mm of rainfall to forecast absent places, essential for climate planning. Our strategy tackles three core difficulties in spatial count data: (i) dispersion that can be either above or below Poisson via a renewal-based Gamma–Count likelihood, (ii) non-linear covariate effects via Bayesian smoothers, and (iii) spatial correlation over irregular domains via thin-plate spline (TPS) fields. Across three datasets, this specification yields improved predictive fit and better-calibrated uncertainty than Poisson and negative-binomial baselines. This reasonable, comprehensible instrument enables researchers in public health, environmental science, and risk assessment to provide insights that foster healthier communities and a more resilient world.