Statistical methods for match probabilities with applications to Y chromosome data

Accurate estimates of Y-STR haplotype frequencies is an interesting problem in itself, but is especially important in forensic genetics, where the frequencies are used to calculate the likelihood ratio (LR) for the evidential weight of a DNA profile found at a crime scene. In this thesis, four methods for Y-STR haplotype frequency estimation are compared with respect to accuracy and bias. This is performed on data from simulated from Wright-Fisher populations with empirical mutation rates and different sampling factors like sample size and the number of markers comprising the haplotypes. Three of the four methods are count based methods (CBMs) and the last method is an allele based method (ABM), defined by if the method represent Y-STR haplotypes as indecomposable objects or not. The first method, named the Count Method (CM) is derived from the empirical frequency of the haplotype. The next two CBMs, the Kappa Model (KM) and the Good-Turing estimator (GTE) are based on the proportion of haplotypes observed a particular number of times in the sample. Last, the Discrete Laplace Method (DLM) identifies subpopulation centers by clustering and models allele frequencies at each loci with discrete Laplace distributions. Hapltotype frequency estimates are then obtained by multiplying estimated allele frequencies across loci. The CBMs underestimated the LR in all scenarios. The DLM have the highest mean accuracy in general, but also have more variance and a tendency to overestimate the LR slightly when haplotypes are composed of more markers. More research into which factors significantly affect haplotype frequency estimates is encouraged