The LR does not exist.

Area of Science:

• Forensic Science
• Probability Theory
• Bayesian Statistics

Background:

• De Finetti's subjective probability theory posits that probability quantifies personal belief.
• Traditional likelihood ratio (LR) calculations assume knowledge of objective population proportions, which are often unknown.
• Estimating population proportions introduces sampling uncertainty, complicating LR interpretation.

Purpose of the Study:

• To apply De Finetti's subjective probability framework to forensic trace evidence analysis.
• To develop a method for assigning evidential value that accounts for uncertainty in population proportion estimates.
• To demonstrate that the evidential value (LR) is determined by knowledge of the proportion, not the unknown proportion itself.

Main Methods:

• Utilizing De Finetti's subjective probability framework.
• Calculating likelihood ratios (LR) based on the degree of belief in population proportions.
• Quantifying evidential information using the logarithm of the LR to encapsulate all uncertainties.

Main Results:

• The evidential value of a shared feature is determined by what is known about the population proportion, not the unknown proportion itself.
• Sampling uncertainty associated with estimated proportions should not be projected onto the LR as an interval.
• A single numerical value, the logarithm of the LR, represents the information gained from the evidence.

Conclusions:

• Probabilistic models provide a robust framework for interpreting the evidential worth of forensic traces.
• The subjective interpretation of probability aligns with the practical assessment of forensic evidence.
• Accurate interpretation of evidence relies on well-defined probabilistic models that encapsulate all relevant uncertainties.