Research on mixed DNA likelihood rate algorithm with suspect samples

This study employed maximum likelihood estimation (MLE) and gamma distribution models to analyze mixed DNA samples containing multiple donor DNAs for 2-, 3-, and 4-person mixture models. The primary objective of DNA mixture analysis is to accurately determine the contribution ratios of each donor within complex mixed samples and to further assess the genetic profiles of each contributor. In this research, DNA peak height data reflect the relative contributions of different donors, which can be influenced by various experimental factors such as PCR amplification effects and DNA concentration, thereby complicating the estimation of mixture proportions. For the 2-person mixture model, we initially applied a gamma distribution to model the DNA peak height data of the mixed sample and utilized the MLE method to optimize parameter estimates, thus accurately determining the relative contribution ratios of the two donors in the sample. As the number of donors increased to 3 or 4, the complexity of the model also escalated, necessitating the use of advanced numerical optimization techniques, including the expectation-maximization (EM) algorithm. Through iterative estimation, the contribution ratios of each donor in the mixture sample were derived. It was assumed that the DNA peak height data of each donor followed a gamma distribution, and the parameters of this distribution were adjusted according to the donor's contribution ratio to derive the overall DNA data distribution of the mixture sample. By employing this analytical approach, the study successfully estimated the contribution ratios of the prosecution and defense in the mixed sample and provided detailed genetic typing information for each contributor. These findings offer significant theoretical support and practical guidance for applications in forensic science, paternity testing, and other fields involving DNA mixture sample analysis. The study highlights that as sample complexity increases, the optimization process becomes increasingly crucial, particularly when handling high-dimensional parameter spaces and large datasets. The selection of appropriate optimization algorithms and the quality of the data are critical factors that significantly influence the accuracy of the results.