Covariance constraints for stochastic inverse problems of computer models

The stochastic inverse problems considered in this article involve estimating the probability distributions of intrinsically random inputs to computer models. These estimations are based on observable outputs affected by model noise. Such problems are increasingly studied in parametric Bayesian frameworks where the parameters of the targeted input distributions are themselves subject to epistemic uncertainties. To enhance the meaningfulness of solutions provided by statistical algorithms — in the sense that forward simulations based on these solutions should yield relevant observables — we derive new prior constraints grounded in the principles of global sensitivity analysis and information theory. Primarily formulated as constraints on covariances in Gaussian linear or linearizable settings, these constraints embody the idea that a valid solution should account for most of the observable uncertainty, with model noise playing only a secondary role. Simulated experiments highlight that incorporating these constraints into stochastic inversion algorithms can indeed reduce the influence of model noise on the outcome. These findings offer promising prospects for extensions to more general frameworks, such as those involving linear Gaussian mixtures.