Expert elicitation and data noise learning for material flow analysis using Bayesian inference

Abstract

Bayesian inference allows the transparent communication and systematic updating of model uncertainty as new data become available. When applied to material flow analysis (MFA), however, Bayesian inference is undermined by the difficulty 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 US 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' informative priors. Sensible, weakly informative priors are 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 and the World Steel Association. The results show a reduction in MFA parametric uncertainty when incorporating the collected data. Only a modest reduction in data noise uncertainty was observed using 2012 data; 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.

Material Flow Analysis of Dysprosium in the United States

“…In other words, the annual domestic demands for each finished product were repeatedly simulated using randomly generated parameters to provide a data range that contained 97.5% of the simulated values. This data range is expected to allow decision-makers to formulate proper policies, for example, adopting results with fewer deviations . Results (Figures S2 and S3 and Table S7) show that the domestic demand for each product has a lower coefficient of variation (approximately 10%), which implies lower volatility of data and thus greater certainty of the results.…”

“…This data range is expected to allow decision-makers to formulate proper policies, 55 for example, adopting results with fewer deviations. 57 Results (Figures S2 and S3 and Table S7) show that the domestic demand for each product has a lower coefficient of variation (approximately 10%), which implies lower volatility of data and thus greater certainty of the results.…”