  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.
