A stochastic partial differential equation for Bayesian spatio-temporal modelling of crime

• Julia Calatayud ^[1] ; Marc Jornet ^[2] ; Javier Platero ^[1] ; Jorge Mateu ^[1]
  1. [1] Universitat Jaume I

     Universitat Jaume I

     Castellón, España

     
  2. [2] Universidad Internacional de La Rioja

     Universidad Internacional de La Rioja

     Logroño, España

     
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 49, Nº. 2, 2025, págs. 149-177
• Idioma: inglés
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• Resumen

  • We propose a stochastic partial differential equation to model geo-referenced data in the plane, with spatially correlated noise and a temporal log-normal evolution. Discretization in space permits us to develop the model in a finite-dimensional framework, reducing it to a set of stochastic differential equations coupled by correlated Wiener processes. The correlations are considered time-varying and stochastic, with a transformed log-normal distribution. The final model is framed within a hierarchical structure, and parameter inference is conducted jointly using Bayesian methods. The statistical methodology is illustrated by analyzing crime activity in the city of Valencia, Spain.