We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use the much criticized Dempster rule of combination, but only the very natural Dempster-Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our setup can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.

中文翻译：

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通过计算置信函数评估法医证据

我们首先讨论用于评估法医证据的经典概率方法的某些问题，特别是它无法区分缺乏信念和怀疑，以及无法模拟给定人群中的完全无知。然后我们讨论 Shafer 置信函数，概率分布的概括，它可以处理这两种反对意见。我们使用信念函数的演算，它不使用备受批评的 Dempster 组合规则，而只使用非常自然的 Dempster-Shafer 条件反射。然后我们将这种微积分应用于一些经典的法医问题，如各种岛屿问题和父母身份识别问题。如果我们除了假设罪魁祸首或父母属于给定的群体（在我们的环境中是可能的）之外不施加任何先验知识，那么当施加统一或其他先验时，我们的答案与经典答案不同。我们实际上可以通过强加相关先验来检索经典答案，因此我们的设置可以而且应该被解释为经典方法的概括，从而提供更大的灵活性。我们展示了如何使用我们的微积分来开发贝叶斯规则的类似物，使用置信函数而不是经典概率。我们还讨论了我们的理论对法律实践的影响。用置信函数代替经典概率。我们还讨论了我们的理论对法律实践的影响。用置信函数代替经典概率。我们还讨论了我们的理论对法律实践的影响。