使用贝叶斯网络对“公平和可持续的福祉”（BES）进行建模：意大利地区的案例研究
Modeling "Equitable and Sustainable Well-being" (BES) using Bayesian Networks: A Case Study of the Italian regions
摘要：
自上世纪末以来，衡量福祉一直是一个备受争议的话题。虽然某些具体方面仍然是悬而未决的问题，但多层面的办法以及建立共同和根深蒂固的指标系统，现已被接受为衡量这一复杂现象的主要途径。这方面的一项有意义的努力是意大利国家统计研究所和国家经济和劳工理事会制定的意大利“公平和可持续福利”指标系统。BES框架包括每年在区域一级测量的一些原子指标，反映不同的福祉领域（例如健康、教育、工作/生活平衡、环境.）。在这项工作中，我们的目标是处理的多维度的BES系统的指标，并试图回答三个主要的研究问题：I）是什么结构的BES原子指标之间的关系; II）是什么结构的BES域之间的关系; III）在何种程度上的关系的结构反映了目前的BES理论框架。我们通过实现贝叶斯网络（BN）来解决这些问题，贝叶斯网络是一种被广泛接受的多变量统计模型，特别适合于处理不确定性推理。BN的实现导致一组节点和一组条件独立语句，它们提供了一个有效的工具来探索变量系统中的关联。在这项工作中，我们还提出了两种策略编码先验知识的BN估计算法，使BES的理论框架可以表示到网络。
英文摘要：
Measurement of well-being has been a highly debated topic since the end of the last century. While some specific aspects are still open issues, a multidimensional approach as well as the construction of shared and well-rooted systems of indicators are now accepted as the main route to measure this complex phenomenon. A meaningful effort, in this direction, is that of the Italian "Equitable and Sustainable Well-being" (BES) system of indicators, developed by the Italian National Institute of Statistics (ISTAT) and the National Council for Economics and Labour (CNEL). The BES framework comprises a number of atomic indicators measured yearly at the regional level and reflecting the different domains of well-being (e.g. Health, Education, Work \& Life Balance, Environment,...). In this work we aim at dealing with the multidimensionality of the BES system of indicators and try to answer three main research questions: I) What is the structure of the relationships among the BES atomic indicators; II) What is the structure of the relationships among the BES domains; III) To what extent the structure of the relationships reflects the current BES theoretical framework. We address these questions by implementing Bayesian Networks (BNs), a widely accepted class of multivariate statistical models, particularly suitable for handling reasoning with uncertainty. Implementation of a BN results in a set of nodes and a set of conditional independence statements that provide an effective tool to explore associations in a system of variables. In this work, we also suggest two strategies for encoding prior knowledge in the BN estimating algorithm so that the BES theoretical framework can be represented into the network.
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