Gaussian Mixture Models of Between-Source Variation for Likelihood Ratio Computation from Multivariate Data.

Area of Science:

• Forensic Science
• Statistical Analysis
• Evidence Evaluation

Background:

• Evaluating trace evidence in forensic science relies on multivariate data analysis.
• The likelihood ratio framework is increasingly used to assess evidence strength.
• Current methods often assume normal distributions for within-source variation and use kernel density functions (KDF) for between-source variation.

Purpose of the Study:

• To present a novel approach for modeling between-source variation in forensic trace evidence analysis.
• To improve the calibration of likelihood ratios by using a Gaussian mixture model (GMM) instead of a KDF.
• To demonstrate the effectiveness of the GMM approach on real-world forensic datasets.

Main Methods:

• Developed a multivariate likelihood ratio framework utilizing a Gaussian mixture model (GMM) to capture between-source variation.
• Modeled both within-source and between-source variations in multivariate forensic data.
• Applied the GMM approach to freely available datasets of inks, glass fragments, and car paints.

Main Results:

• The Gaussian mixture model (GMM) approach demonstrated improved performance in modeling between-source variation compared to the traditional kernel density function (KDF).
• Likelihood ratios generated using the GMM approach were better calibrated, as indicated by a lower log-likelihood ratio cost (Cllr).
• The method showed effectiveness across diverse trace evidence types, including inks, glass, and car paints.

Conclusions:

• The Gaussian mixture model (GMM) offers a more accurate and robust method for calculating likelihood ratios in forensic science.
• This approach enhances the reliability of evidence evaluation by better capturing the complexities of between-source variation.
• The findings suggest a significant advancement in statistical methods for forensic trace evidence analysis.