A Two-Stage Bayesian Framework for Multi-Fidelity Sequential Updating of Spatial Fragility Fields
Abstract
This paper develops a Bayesian framework for updating event-conditioned spatial fragility fields by combining physics-informed priors with incrementally available post-disaster observations. The framework supports sequential refinement of regional vulnerability estimates as additional post-disaster evidence becomes available. The framework reformulates physics-informed fragility estimates into a Probit-Normal (PN) representation that captures aleatory variability and epistemic uncertainty in an analytically tractable form. Stage 1 performs local Bayesian updating by moment-matching PN marginals to Beta surrogates that preserve their probability shapes, enabling conjugate Beta-Bernoulli updates with soft, multi-fidelity observations. Fidelity weights encode source reliability, and the resulting Beta posteriors are re-projected into PN form, producing heteroscedastic fragility estimates whose variances reflect data quality and coverage. Stage 2 assimilates the heteroscedastic pseudo-observations through an ordered probit-warped Gaussian Process (GP) that propagates information across space and structural archetypes. A shared latent spatial severity field and strictly positive threshold-gap functions enforce pathwise ordering of exceedance probabilities and yield nonnegative exact damage-state probabilities. The framework is applied to the 2011 Joplin tornado, where wind-field priors and computer-vision damage assessments are fused under varying assumptions about tornado width, sampling strategy, and observation completeness. Controlled synthetic experiments and the Joplin application show that the framework can reduce the influence of biased priors as evidence accumulates, propagate locally updated information into unobserved regions, and produce uncertainty-aware, ordinally valid exceedance and exact damage-state probability fields.