Exclusion probabilities and likelihood ratios with applications to mixtures

Area of Science:

• Forensic Science
• Statistics
• Genetics

Background:

• Statistical evidence in forensic casework, particularly from mixed DNA profiles, is crucial.
• Likelihood ratio (LR) and Random Man Not Excluded (RMNE) probability are common summary statistics.
• Existing literature debates the advantages and disadvantages of LR and exclusion probabilities.

Purpose of the Study:

• To clarify the debate surrounding likelihood ratios and exclusion probabilities in forensic DNA analysis.
• To demonstrate the mathematical relationship between RMNE and LR in mixture cases.
• To address the impact of artefacts like dropout and drop-in on these statistical measures.

Main Methods:

• Proving a general mathematical relationship between RMNE and LR.
• Viewing the likelihood ratio as a random variable to derive new properties.
• Applying a binary model to illustrate results, including dropout and drop-in scenarios.

Main Results:

• RMNE can be expressed as an average of the LR, indicating expected LR is at least 1/RMNE for contributors.
• New general properties for mixture cases are established.
• Methods for estimating exceedance probabilities of LR for non-donors are demonstrated, with RMNE as a specific case.

Conclusions:

• The study provides a unified framework for understanding statistical evidence in forensic DNA mixtures.
• The findings enhance the interpretation of mixture evidence, especially in the presence of dropout and drop-in.
• This work clarifies the relationship between LR and RMNE, offering practical implications for casework.