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<p>Environmental spatio-temporal data often exhibit nonlinear dynamics, nonstationarity, and positive skewness, which can limit the adequacy of Gaussian random-field models. We propose a Bayesian neural field framework that combines a coordinate-based neural representation for the mean with flexible closed skew-normal residuals and a separable space–time correlation structure. This formulation enables scalable posterior inference via variational methods and yields probabilistic predictive uncertainty for large datasets. Simulation experiments show that simpler models are preferred when the data-generating mechanism is linear and Gaussian, whereas the neural-field component improves recovery under nonlinear space–time interactions and the flexible closed skew-normal component improves upper-tail calibration under skewness. In a matched-data benchmark, mean-field variational inference gives point predictions close to No-U-Turn sampler but understates part of the posterior dispersion. An application to monthly averages of the daily PM<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(_{2.5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>2.5</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>-based AQI sub-index in Tehran (2014–2024), evaluated using completely held-out monitoring stations in 2024, illustrates the practical predictive framework. The proposed approach offers a unified Bayesian formulation for nonlinear spatio-temporal structure and asymmetric residual behavior.</p>

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Bayesian neural fields for skewed spatio–temporal data via variational inference: an application to monthly PM\(_{2.5}\)-based AQI in Tehran

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Fatemeh Hosseini,
  • Omid Karimi

摘要

Environmental spatio-temporal data often exhibit nonlinear dynamics, nonstationarity, and positive skewness, which can limit the adequacy of Gaussian random-field models. We propose a Bayesian neural field framework that combines a coordinate-based neural representation for the mean with flexible closed skew-normal residuals and a separable space–time correlation structure. This formulation enables scalable posterior inference via variational methods and yields probabilistic predictive uncertainty for large datasets. Simulation experiments show that simpler models are preferred when the data-generating mechanism is linear and Gaussian, whereas the neural-field component improves recovery under nonlinear space–time interactions and the flexible closed skew-normal component improves upper-tail calibration under skewness. In a matched-data benchmark, mean-field variational inference gives point predictions close to No-U-Turn sampler but understates part of the posterior dispersion. An application to monthly averages of the daily PM \(_{2.5}\) 2.5 -based AQI sub-index in Tehran (2014–2024), evaluated using completely held-out monitoring stations in 2024, illustrates the practical predictive framework. The proposed approach offers a unified Bayesian formulation for nonlinear spatio-temporal structure and asymmetric residual behavior.