Mixed effects modelling for glass category estimation from glass refractive indices

Area of Science:

• Forensic Science
• Materials Science
• Statistical Modeling

Background:

• Glass fragments are crucial forensic evidence.
• Characterizing glass properties aids in source attribution.
• Refractive index is a key property for glass analysis.

Purpose of the Study:

• To model and estimate the change in refractive index of glass fragments after re-annealing.
• To assess the evidential value of glass fragments based on refractive index changes.
• To compare the performance of kernel density estimates and log-concave estimation for modeling refractive index changes.

Main Methods:

• Measurement of refractive indexes of 520 glass fragments from 105 items (containers, windows, automobile glass).
• Model-based estimation of refractive index change after re-annealing.
• Application of kernel density estimates and log-concave estimation to model refractive index change distributions.
• Calculation of evidential value based on estimated refractive index changes.

Main Results:

• Simplified estimation methods were found equivalent to a full model for refractive index change.
• Kernel density estimates and log-concave estimation provided good estimates of glass category.
• Kernel density estimates showed slightly better performance across all metrics compared to log-concave estimates.
• Normal distribution models were inadequate for refractive index changes in two glass categories.

Conclusions:

• Refractive index change after re-annealing is a valuable metric for forensic glass analysis.
• Kernel density estimation is a robust method for classifying glass fragments.
• Log-concave estimation offers qualitative advantages despite slightly lower performance metrics.
• Further research into advanced statistical methods for glass analysis is warranted.