  Bayesian inference allows the transparent communication of uncertainty in
material flow analyses (MFAs), and a systematic update of uncertainty as new
data become available. However, the method is undermined by the difficultly of
defining proper priors for the MFA parameters and quantifying the noise in the
collected data. We start to address these issues by first deriving and
implementing an expert elicitation procedure suitable for generating MFA
parameter priors. Second, we propose to learn the data noise concurrent with
the parametric uncertainty. These methods are demonstrated using a case study
on the 2012 U.S. steel flow. Eight experts are interviewed to elicit
distributions on steel flow uncertainty from raw materials to intermediate
goods. The experts' distributions are combined and weighted according to the
expertise demonstrated in response to seeding questions. These aggregated
distributions form our model parameters' prior. A sensible, weakly-informative
prior is also adopted for learning the data noise. Bayesian inference is then
performed to update the parametric and data noise uncertainty given MFA data
collected from the United States Geological Survey (USGS) and the World Steel
Association (WSA). The results show a reduction in MFA parametric uncertainty
when incorporating the collected data. Only a modest reduction in data noise
uncertainty was observed; however, greater reductions were achieved when using
data from multiple years in the inference. These methods generate transparent
MFA and data noise uncertainties learned from data rather than pre-assumed data
noise levels, providing a more robust basis for decision-making that affects
the system.
