When evaluating DNA evidence within a likelihood ratio framework, should the propositions be exhaustive?

Area of Science:

• Forensic Science
• Genetics
• Probability Theory

Background:

• Casework often involves limited initial information for forming propositions.
• Exhaustive propositions are ideal for accurate DNA evidence evaluation.
• Incomplete proposition sets risk misinterpreting likelihood ratios (LR).

Purpose of the Study:

• To develop a rational approach for forming propositions in DNA analysis with limited information.
• To address the theoretical risks associated with non-exhaustive propositions in casework.
• To improve the discrimination power of DNA evidence through refined proposition formulation.

Main Methods:

• Mathematical analysis of likelihood ratios (LR) under various proposition scenarios.
• Investigating the impact of neglecting small probability terms in LR calculations.
• Applying weighted averaging of LRs based on the number of contributors (NoC) and background information.

Main Results:

• DNA contributor presence can be assumed under both prosecution (Hp) and alternative (Ha) propositions if prior probability is reasonable and profile supports inclusion.
• Dominant terms in LR calculations justify assuming contributor presence under key propositions.
• Suggests assuming one person of interest (POI) when examining another in mixed DNA profiles if collectively they explain the profile.

Conclusions:

• A rational approach to proposition formation enhances DNA evidence evaluation in casework.
• The proposed method improves discrimination by considering more meaningful propositions.
• The overall LR is a weighted average of LRs with the same number of contributors, influenced by profile probability and background information.