Department of Economics and Business Economics, Aarhus University, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark.
Department of Economics and Business Economics, Aarhus University, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark.
Waste Manag. 2021 May 15;127:90-100. doi: 10.1016/j.wasman.2021.04.011. Epub 2021 Apr 29.
Prediction of waste production is an essential part of the design and planning of waste management systems. The quality and applicability of such predictions depend heavily on model assumptions and the structure of the collected data. Ordinarily, municipal waste generation data are organized in hierarchical structures with municipal or county levels, and multilevel models can be used to generalize linear regression by directly incorporating the structure into the model. However, small amounts of data can limit the applicability of multilevel models and provide biased estimates. To cope with this problem, Bayesian estimation is often recommended as an alternative to frequentist estimation, such as least squares or maximum likelihood estimation. This paper proposes a multilevel framework under a Bayesian approach to model municipal waste generation with hierarchical data structures. Using a real-world dataset of municipal waste generation in Denmark, the predictive accuracy of multilevel models is compared to aggregated and disaggregated Bayesian models using socio-economic external variables. Results show that Bayesian multilevel models outperform the other models in prediction accuracy, based on the leave-one-out information criterion. A comparison of the Bayesian approach with its frequentist alternative shows that the Bayesian model is more conservative in coefficient estimation, with estimates shrinking to the grand mean and broader credible intervals, in contrast with narrower confidence intervals produced by the frequentist models.
垃圾产生量的预测是垃圾管理系统设计和规划的重要组成部分。此类预测的质量和适用性在很大程度上取决于模型假设和所收集数据的结构。通常，城市垃圾产生数据采用具有市级或县级的层次结构进行组织，并且可以使用多层次模型通过直接将结构纳入模型来推广线性回归。然而，少量的数据可能会限制多层次模型的适用性并提供有偏差的估计。为了解决这个问题，贝叶斯估计通常被推荐作为频率派估计（如最小二乘法或最大似然估计）的替代方法。本文提出了一种基于贝叶斯方法的多层次框架，用于对具有层次数据结构的城市垃圾产生进行建模。使用丹麦城市垃圾产生的实际数据集，使用社会经济外部变量比较了多层次模型与聚合和离散贝叶斯模型的预测准确性。结果表明，基于留一信息准则，贝叶斯多层次模型在预测准确性方面优于其他模型。贝叶斯方法与频率派方法的比较表明，贝叶斯模型在系数估计方面更为保守，估计值收缩到总平均值和更宽的置信区间，而频率派模型则产生更窄的置信区间。
