Hierarchical Bayes for the Explicit Estimation of Model Prediction Errors

An extensive research effort is dedicated to Bayesian estimation methods for analyzing the empirical behaviour of structures. State-of-the-art structural identification methods currently quantify model uncertainties by estimating hyper-parameters for the prediction-error prior. This paper exposes that this uncertainty quantification procedure does not fully recognize the epistemic nature of model prediction errors, because their posterior probability density function (PDF) is not explicitly estimated and their interaction with model parameters are not considered. This paper presents a Hierarchical Bayes formulation for estimating the joint posterior PDF of model parameters and prediction errors. This Hierarchical Bayes approach allows capturing the dependencies between unknown model parameters and unknown prediction errorsit offers a more accurate picture of the structural behaviour than when estimating the prior hyper-parameters alone. The application of this method to large-scale structures requires an adequate model the for the prediction-error prior, which remains a case-specific challenge