Building Population-Informed Priors for Bayesian Inference Using Data-Consistent Stochastic Inversion (2407.13814v3)

Abstract: Bayesian inference provides a powerful tool for leveraging observational data to inform model predictions and uncertainties. However, when such data is limited, Bayesian inference may not adequately constrain uncertainty without the use of highly informative priors. Common approaches for constructing informative priors typically rely on either assumptions or knowledge of the underlying physics, which may not be available in all scenarios. In this work, we consider the scenario where data are available on a population of assets/individuals, which occurs in many problem domains such as biomedical or digital twin applications, and leverage this population-level data to systematically constrain the Bayesian prior and subsequently improve individualized inferences. The approach proposed in this paper is based upon a recently developed technique known as data-consistent inversion (DCI) for constructing a pullback probability measure. Succinctly, we utilize DCI to build population-informed priors for subsequent Bayesian inference on individuals. While the approach is general and applies to nonlinear maps and arbitrary priors, we prove that for linear inverse problems with Gaussian priors, the population-informed prior produces an increase in the information gain as measured by the determinant and trace of the inverse posterior covariance. We also demonstrate that the Kullback-Leibler divergence often improves with high probability. Numerical results, including linear-Gaussian examples and one inspired by digital twins for additively manufactured assets, indicate that there is significant value in using these population-informed priors.