Material Flow Analysis (MFA) is used to quantify and understand the life cycles of materials from production to end of use, which enables environmental, social and economic impacts and interventions. MFA is challenging as available data is often limited and uncertain, leading to an underdetermined system with an infinite number of possible stocks and flows values. Bayesian statistics is an effective way to address these challenges by principally incorporating domain knowledge, and quantifying uncertainty in the data and providing probabilities associated with model solutions. This paper presents a novel MFA methodology under the Bayesian framework. By relaxing the mass balance constraints, we improve the computational scalability and reliability of the posterior samples compared to existing Bayesian MFA methods. We propose a mass based, child and parent process framework to model systems with disaggregated processes and flows. We show posterior predictive checks can be used to identify inconsistencies in the data and aid noise and hyperparameter selection. The proposed approach is demonstrated on case studies, including a global aluminium cycle with significant disaggregation, under weakly informative priors and significant data gaps to investigate the feasibility of Bayesian MFA. We illustrate just a weakly informative prior can greatly improve the performance of Bayesian methods, for both estimation accuracy and uncertainty quantification.

翻译：物质流分析（MFA）用于量化和理解材料从生产到最终使用的生命周期，从而评估其环境、社会与经济影响并制定干预措施。MFA面临挑战，因为可用数据通常有限且不确定，导致系统欠定，存在无限种可能的存量与流量值。贝叶斯统计学是应对这些挑战的有效方法，它能够从原理上整合领域知识，量化数据的不确定性，并提供与模型解相关的概率。本文提出了一种贝叶斯框架下的新型MFA方法。通过放宽质量平衡约束，与现有贝叶斯MFA方法相比，我们提高了后验样本的计算可扩展性和可靠性。我们提出了一个基于质量、包含子过程与父过程的框架，以建模具有分解过程和流量的系统。我们展示了后验预测检查可用于识别数据中的不一致性，并辅助噪声与超参数的选择。所提出的方法通过案例研究进行了验证，包括一个具有显著分解度的全球铝循环案例，在弱信息先验和显著数据缺失条件下，探讨了贝叶斯MFA的可行性。我们证明，即使是弱信息先验也能极大提升贝叶斯方法的性能，无论是在估计精度还是不确定性量化方面。