基于多元玻璃物证的非平衡似然比比对检验模型建立及评估
Establishment and Evaluation of Non-Equilibrium Likelihood Ratio Comparison Test Model Based on Multi-Element Glass Physical Evidence

对在犯罪现场和嫌疑人身上发现的证据特征进行测量和评估是刑事调查中的重要部分。Aitken等在2006年提出了样本平衡的多元正态分布三层次证据似然比模型。基于玻璃数据，本文考虑了一种非平衡类型的多元正态三层次证据：包含7种元素的玻璃碎片数据58组，其中每组包含的玻璃样本数量不同(样本非平衡性)；共有396个玻璃样本，每个样本都被测量4次。为降低数据维度，利用图形模型(graphical models)找出具有高度相关的变量。假定数据服从多元正态分布，建立样本非平衡的多元正态分布三层次证据似然比模型。在58对同一来源对比中，$LR>1$ 的有20对，假阴性率约为34.48%；在1653对不同来源对比中，$LR>1$ 的有78对，假阳性率约为4.7%。对于司法机关来说，评价的假阳性率更为重要，因为假阳性结果是对应于对无辜者的证据。本文建立的基于图形模型的非平衡似然比建模为司法科学中解决非平衡数据提供了一种新的方案。
In criminal investigation, the measurement and evaluation of the characteristics of the evidence found at the crime scene and on the suspect is an important part. Aitken et al. proposed a multivariate normal distribution three-level evidence likelihood ratio model with sample balance in 2006. Based on the glass data, we consider a non-equilibrium type of multivariate normal three-level evidence: 58 sets of glass fragment data containing 7 elements, each of which contains a different number of glass samples (sample non-equilibrium). There were 396 glass samples, each of which was measured four times. To reduce the dimensionality of the data, graphical models are used to find variables with high correlation. In the 58 pairs from the same source, there were 20 pairs $LR>1$ , and the false negative rate was about 34.48%. In the comparison of 1653 pairs from different sources, there were 78 pairs $LR>1$ , and the false positive rate was about 4.7%. For the prosecution, the false positive rate of the evaluation is more important because false positive results correspond to evidence against an innocent person. The non-equilibrium likelihood ratio modeling based on graphical model constructed in this paper provides a new scheme for solving non-equilibrium data in forensic science.