讲座题目：Make Evidence Theory Probabilistic Again（重塑证据理论的概率本质）

主讲人：徐冬玲 英国曼彻斯特大学 Alliance 曼彻斯特商学院决策科学与系统讲席教授

讲座时间：2025年04月28日14:30

讲座地点：学院210

讲座摘要：

Since Dempster proposed his rule for evidence combination, he consistently maintained that it extends Bayes’ rule for statistical inference in situations where probabilities are imprecisely known. However, the development of evidence theory, also known as Dempster-Shafer theory of evidence, diverged from its probabilistic roots. Some researchers have argued that Dempster’s rule is not Bayesian, or only Bayesian under specific conditions, such as when the prior is uniform.

Over the past few decades, our research has focused on the Evidential Reasoning (ER) rule for evidence combination, emphasizing its probabilistic nature and its relationships with Bayes’ rule, Dempster’s rule, and Shafer’s rule. We have proven that Dempster’s rule is inherently probabilistic, serving as an extension of Bayes’ rule, and becomes equivalent to Bayes’ rule when precise probabilities are available. Furthermore, we have demonstrated that the ER rule is also probabilistic and includes Bayes’ rule and Dempster’s rule as special cases.

In this talk, we will also explain the differences between the ER rule and Shafer’s discounting rule. We will explore when Shafer’s rule retains its probabilistic nature and when it does not, conjecturing that Shafer’s original intention was to maintain this probabilistic foundation. Additionally, we will address some criticisms of Dempster’s rule in early literature, identifying instances where such critiques were incorrect or misapplied. We argue that the deviation of evidence theory from its probabilistic trajectory was unintentional. The motivation behind our efforts to re-establish evidence theory’s probabilistic foundation is our belief that probability is more universally interpretable than alternative measures, such as possibility degrees.

Finally, we will discuss Dempster’s rule’s requirement for independence among evidence sources and clarify what independence entails using real-world examples.

自邓普斯特（Dempster）提出证据合成规则以来，他始终认为该规则是统计推理中贝叶斯规则在概率信息不精确场景下的扩展。然而，证据理论（即邓普斯特-谢弗证据理论）的发展逐渐偏离了其概率根源。部分研究者提出，邓普斯特规则并非贝叶斯式的，或仅在特定条件（如先验均匀分布）下具有贝叶斯属性。过去数十年，我们的研究聚焦于证据推理（ER）合成规则，着重揭示其概率本质及其与贝叶斯规则、邓普斯特规则和谢弗规则的关联。我们证明：邓普斯特规则本质上是概率性的，作为贝叶斯规则的扩展，在精确概率可用时与贝叶斯规则等价；进一步表明，ER 规则同样具有概率属性，并将贝叶斯规则和邓普斯特规则纳入其特例范畴。本报告还将阐释 ER 规则与谢弗折扣规则的差异，探讨谢弗规则何时保留概率本质、何时偏离，并推测谢弗的初衷是维持这一概率基础。同时，针对早期文献中对邓普斯特规则的若干批评，我们将指出其中存在的错误或误用情形，论证证据理论偏离概率轨迹并非本意。我们致力于重构证据理论概率基础的动机在于：概率相较于可能性度等其他测度，具有更普适的解释性。最后，报告将讨论邓普斯特规则对证据源独立性的要求，结合实际案例阐明“独立性”的具体内涵。

主讲人简介：

徐冬玲，现任英国曼彻斯特大学 Alliance 曼彻斯特商学院决策科学与系统讲席教授。三十年来，她在不确定性下的数据分析、统计推理、机器学习、决策支持系统，以及系统与过程建模、统计故障检测等领域开展了深入研究，并推动其在多领域的应用。她与杨剑波教授共同开发多个基于网页的交互式决策支持系统及 Windows 平台智能决策系统（IDS）软件。该软件通过证据推理方法，支持处理随机性、主观判断、模糊信息、数据缺失等多种不确定性形式的多准则决策分析，无需删除或扭曲不确定数据。

徐教授研发的统计故障检测系统已被通用汽车、乐购、英国国家医疗服务体系（NHS）、福特、壳牌、英国石油、中国海油等机构广泛采用，应用领域涵盖医疗健康、金融、系统安全分析及组织质量管理自我评估。其证据推理方法与 IDS 软件已被全球50余个国家的从业者和研究者使用。她发表100余篇同行评审期刊论文、著作章节及专著，研究成果对多个行业的决策制定与风险评估实践产生了重要影响。