AI 中文总结
针对法医稀有类型匹配问题，提出贝叶斯决策论框架，用对数评分规则量化九种似然比方法的预期成本，并通过经验验证提供方法选择指南。
AI 中文摘要
稀有类型匹配问题是法医统计学家面临的一个具有挑战性的情况，其目标是在犯罪斑迹的某一特征与嫌疑人斑迹的相应特征匹配且该特征此前未被观察到时，提供该匹配的价值。文献中已设计了多种方法来评估稀有类型匹配情形下的似然比，此时证据包括在犯罪现场发现的与指定嫌疑人的Y-STR谱型匹配的Y-STR谱型。我们开发了一个通用的贝叶斯决策论框架，用于使用对数评分规则量化替代方法的预期成本。该框架提供了后验交叉熵的一种新颖形式化，明确增强了用于从数据中提取信息的方法特定策略的贡献。我们重新审视了后验交叉熵的现有分解，并引入了一种新的互补分解，该分解为此贡献提供了更具可解释性的表征。本研究通过使用经验验证实验评估九种不同方法的性能来比较它们。其最终目标是为法医专家和事实认定者提供方法论见解以及这些替代方法的实验前指南。
英文摘要
The rare type match problem is a challenging situation faced by a forensic statistician who aims at providing the value of a match between some characteristic of a crime stain and the corresponding characteristic of a suspect's stain when this characteristic has not been observed before. Several methods have been designed in the literature to assess likelihood ratios for the rare type match case when evidence consists of a Y-STR profile found on the crime scene matching the Y-STR profile of a designated suspect. We develop a general Bayesian decision-theoretic framework for quantifying the expected cost of alternative approaches using the logarithmic scoring rule. The framework provides a novel formalization of the posterior cross-entropy, which explicitly enhances the contribution of the method-specific strategy used to extract information from the data. We revisit existing decompositions of posterior cross-entropy and introduce a new complementary decomposition that provides a more interpretable characterization of this contribution. This work compares nine different methods by assessing their performance using empirical validation experiments. Its ultimate goal is to provide forensic experts and triers of fact with methodological insight and a pre-experimental guide to these alternative approaches.
