A solution to the static frame validation challenge problem using Bayesian model selection

We provide a solution to the static frame validation challenge problem (see this issue) in a manner that is consistent with the guidelines provided by the Validation Challenge Workshop tasking document. The static frame problem is constructed such that variability in material properties is known to be the only source of uncertainty in the system description, but there is ignorance on the type of model that best describes this variability. Hence both types of uncertainty, aleatoric and epistemic, are present and must be addressed. Our approach is to consider a collection of competing probabilistic models for the material properties, and calibrate these models to the information provided; models of different levels of complexity and numerical efficiency are included in the analysis. A Bayesian formulation is used to select the optimal model from the collection, which is then used for the regulatory assessment. Bayesian credible intervals are used to provide a measure of confidence to our regulatory assessment.