March 2024 Density-based matching rule: Optimality, estimation, and application in forensic problems
Hana Lee, Yumou Qiu, Alicia Carriquiry, Danica Ommen
Author Affiliations +
Ann. Appl. Stat. 18(1): 770-793 (March 2024). DOI: 10.1214/23-AOAS1812


We consider matching problems where the goal is to determine whether two observations randomly drawn from a population with multiple (sub)groups are from the same (sub)group. This is a key question in forensic science, where items with unidentified origins from suspects and crime scenes are compared to objects from a known set of sources to see if they originated from the same source. We derive the optimal matching rule under known density functions of data that minimizes the decision error probabilities. Empirically, the proposed matching rule is computed by plugging parametrically estimated density functions using training data into the formula of the optimal matching rule. The connections between the optimal matching rule and existing methods in forensic science are explained. In particular, we contrast the optimal matching rule to classification and also compare it to a score-based approach that relies on similarity features extracted from paired items. Numerical simulations are conducted to evaluate the proposed method and show that it outperforms the existing methods in terms of a higher ROC curve and higher power to identify matched pairs of items. We also demonstrate the utility of the proposed method by applying it to a real forensic data analysis of glass fragments.

Funding Statement

Lee, Carriquiry and Ommen were partially funded by the Center for Statistics and Applications in Forensic Evidence (CSAFE) through Cooperative Agreements 70NANB15H176 and 70NANB20H019 between NIST and Iowa State University, which includes activities carried out at Carnegie Mellon University, Duke University, University of California Irvine, University of Virginia, West Virginia University, University of Pennsylvania, Swarthmore College, and University of Nebraska, Lincoln.


The authors would like to thank the anonymous referees, an Associate Editor, and the Editor for their constructive comments that improved the quality of this paper. Part of the work reported in the paper was conducted while Yumou Qiu was affiliated with Iowa State University. He thanks ISU’s statistics department for providing various support during the course of the project. Yumou Qiu is the corresponding author.


Download Citation

Hana Lee. Yumou Qiu. Alicia Carriquiry. Danica Ommen. "Density-based matching rule: Optimality, estimation, and application in forensic problems." Ann. Appl. Stat. 18 (1) 770 - 793, March 2024.


Received: 1 April 2023; Revised: 1 August 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1812

Keywords: ‎classification‎ , Forensic science , likelihood ratio , Matching , optimal decision rule

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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