Analytical Extraction of Conditional Aleatory Sensitivities Across Epistemic Space via a Single PCE Model

In hybrid uncertainty quantification, evaluating how aleatory sensitivities vary under epistemic uncertainty, referred to as conditional Sobol' indices, is typically hindered by the computationally expensive double-loop procedure.

Classical Polynomial Chaos Expansion (PCE) provides efficient access to global sensitivity measures but cannot directly resolve sensitivity variation across the epistemic space without repeated surrogate reconstruction.

This study proposes a unified Bayesian framework that extracts continuous conditional Sobol' fields from a single global PCE representation.

By exploiting the tensor-product structure of orthogonal polynomial bases in an augmented stochastic space, the global expansion is analytically decomposed into epistemic-dependent coefficient fields, enabling a closed-form variance decomposition.

As a result, conditional Sobol' indices can be computed through a purely algebraic post-processing step without additional model evaluations or retraining.

In addition, a Reversible Jump Markov Chain Monte Carlo (RJMCMC) scheme is incorporated to perform adaptive basis selection and trans-dimensional inference, while simultaneously providing Bayesian credible intervals for the conditional sensitivity measures.

Numerical experiments on a high-dimensional groundwater flow model demonstrate that the proposed method significantly reduces computational cost while maintaining smooth sensitivity fields and statistically consistent uncertainty quantification across the epistemic domain.