Statistical models for firearm and tool mark image comparisons based on the congruent matching cells (CMC) method

Area of Science:

• Forensic Science
• Firearm Evidence Identification
• Ballistics

Background:

• The congruent matching cells (CMC) method is used in firearm evidence identification to compare topography images of breech face impressions.
• CMC analysis quantifies similarity by determining correlated cell pairs and identifying congruent match cells (CMC pairs).
• Accurate estimation of error rates and likelihood ratios (LR) requires appropriate probability distributions for CMC results.

Purpose of the Study:

• To discuss statistical models for CMC measurements, including binomial and related distributions.
• To address the limitation of previous studies assuming a constant number of Bernoulli trials (N) in CMC analysis.
• To introduce a generalized frequency function for CMC values and provide its limiting distribution, accommodating variable N.

Main Methods:

• Discussion of four statistical models for CMC measurements: binomial and three binomial-related distributions.
• Introduction of a generalized frequency function to model CMC values when the number of cell pairs (N) varies.
• Application of nonlinear regression models to estimate parameters using actual CMC values from fired cartridge cases.

Main Results:

• The generalized frequency function effectively depicts the behavior of CMC values, especially when N varies between image pairs.
• The limiting distribution of the generalized frequency function is provided for theoretical analysis.
• Nonlinear regression models successfully estimated parameters using real-world CMC data from firearm evidence.

Conclusions:

• The proposed generalized frequency function offers a more appropriate statistical framework for CMC measurements in firearm identification.
• This methodology improves the reliability of quantifying topography similarity and estimating error rates in forensic firearm analysis.
• The study provides a robust statistical approach for analyzing CMC data from fired cartridge cases.