Title: The effect of prior probabilities on quantification and propagation of imprecise probabilities resulting from small datasets,
Abstract: This paper outlines a methodology for Bayesian multimodel uncertainty
quantification (UQ) and propagation and presents an investigation into the
effect of prior probabilities on the resulting uncertainties. The UQ
methodology is adapted from the information-theoretic method previously
presented by the authors (Zhang and Shields, 2018) to a fully Bayesian
construction that enables greater flexibility in quantifying uncertainty in
probability model form. Being Bayesian in nature and rooted in UQ from small
datasets, prior probabilities in both probability model form and model
parameters are shown to have a significant impact on quantified uncertainties
and, consequently, on the uncertainties propagated through a physics-based
model. These effects are specifically investigated for a simplified plate
buckling problem with uncertainties in material properties derived from a small
number of experiments using noninformative priors and priors derived from past
studies of varying appropriateness. It is illustrated that prior probabilities
can have a significant impact on multimodel UQ for small datasets and
inappropriate (but seemingly reasonable) priors may even have lingering effects
that bias probabilities even for large datasets. When applied to uncertainty
propagation, this may result in probability bounds on response quantities that
do not include the true probabilities.