Efficient computations with the likelihood ratio distribution.

Area of Science:

• Forensic Genetics
• Statistical Genetics
• Computational Biology

Background:

• Determining the probability of a likelihood ratio exceeding a threshold is essential for forensic applications like kinship testing and familial searching.
• Existing methods for calculating this probability, such as simulation, discrete approximation, and normal approximation, have limitations including computational intensity or providing only bounds.
• Exact computation algorithms exist but are often computationally intensive for large datasets.

Purpose of the Study:

• To develop novel, efficient, and accurate methods for computing the exceedance probability of a likelihood ratio in forensic genetics.
• To improve upon existing simulation techniques and exact computation algorithms for likelihood ratio threshold exceedance.

Main Methods:

• Enhanced simulation using importance sampling for increased efficiency.
• A novel, exact, and fast algorithm for computing exceedance probabilities.
• A hybrid approach combining the novel algorithm with a discrete approximation for handling very large problems and providing bounds.

Main Results:

• Importance sampling significantly improves the efficiency of simulation-based exceedance probability calculations.
• The novel algorithm provides exact, fast computations for moderately large problems.
• The hybrid approach effectively handles very large problems, yielding lower and upper bounds on the exceedance probability.

Conclusions:

• The presented methods offer significant improvements in efficiency and accuracy for calculating likelihood ratio exceedance probabilities in forensic genetics.
• These approaches are applicable to critical forensic tasks including kinship testing, familial searching, and mixture interpretation.
• The developed algorithms are implemented in the freely available R-package DNAprofiles.