The multivariate Dirichlet-multinomial distribution and its application in forensic genetics to adjust for...

Area of Science:

• Statistics
• Forensic Genetics
• Population Genetics

Background:

• The Dirichlet-multinomial distribution is a key statistical model.
• Forensic genetics uses the θ-correction for remote ancestry adjustments in DNA mixture analysis.
• Bayesian networks offer efficient likelihood ratio computations in forensic genetics.

Purpose of the Study:

• To construct a multivariate generalization of the Dirichlet-multinomial distribution.
• To incorporate the θ-correction into Bayesian networks for forensic genetic analysis.
• To evaluate the impact of the θ-correction on the weight of evidence for rare genotypes.

Main Methods:

• Construction of a multivariate Dirichlet-multinomial distribution.
• Modification of the Markov structure in Bayesian networks to include the θ-correction.
• Numerical examples to demonstrate the effect of the θ-correction.

Main Results:

• The proposed multivariate distribution extends the Dirichlet-multinomial model.
• Incorporation of the θ-correction into Bayesian networks enhances realistic population genetic modeling.
• The θ-correction significantly affects the weight of evidence, particularly for rare alleles and genotypes.

Conclusions:

• The developed multivariate Dirichlet-multinomial distribution provides a more realistic model for forensic DNA mixture analysis.
• Integrating the θ-correction within Bayesian networks improves the statistical rigor of forensic genetic evidence evaluation.
• This approach offers a more accurate assessment of match probabilities, accounting for population substructure.