Evaluation of PSHA logic trees considering the Pólya distribution to model the spatial correlation between observation sites

Probabilistic Seismic Hazard Analysis (PSHA) is the standard methodology for estimating the likelihood of exceeding ground-motion intensity thresholds at a given site, accounting for both aleatory and epistemic uncertainties. Despite its widespread adoption, PSHA remains subject to criticism due to the high uncertainty in its predictions and the limited availability of observational data for validation. This study proposes a novel framework for the direct evaluation and Bayesian updating of PSHA logic-tree weights using observed ground-motion records, explicitly addressing spatial correlation among multiple observation sites. The methodology combines event-based simulations of branch-consistent ground-motion fields, site-effect corrections, and operational-period modeling to ensure comparability with empirical data. Correlated exceedance counts are modeled using the Pólya (negative binomial) distribution, which captures variance inflation induced by spatial dependence. At the same time, joint multi-IML updating employs a Bernstein copula to represent dependence across intensity measure levels. The framework is applied to a PSHA model for metropolitan France using a reference database spanning 1977–2020 and comprising EDF industrial sites and EPOS-France stations. Results confirm the adequacy of the Pólya distribution for correlated exceedance modeling, with spatial correlation observed consistently at monthly resolution. EDF sites provide nearly the same effective observation time as the full network due to their wide spatial distribution, while EPOS-France stations contribute limited additional statistical power because of clustering. Bayesian updating improves model consistency, particularly when applied jointly across multiple IMLs, and highlights systematic overestimation at low thresholds. Sensitivity analyses reveal that uncertainties in station operability influence results but do not fully explain discrepancies between predicted and observed exceedances. This correlation-aware, multi-IML evaluation framework enhances the statistical robustness of PSHA validation and provides a principled approach for data-informed logic-tree weighting, offering clear pathways for methodological refinement and regulatory application.