Forensic laboratories use lengths of fragments from several locations of human DNA to decide whether a sample of body fluid left at the scene of a crime came from a suspect or whether a sample recovered from a suspect's clothing is the victim's. Using an inferential approach called "match/binning," they first decide whether there is a match between the lengths of DNA fragments from the suspect and crime samples. If there is a match, they then calculate a "match proportion." This is the proportion of a data base of DNA fragment lengths that would similarly match, that is, occur in an interval or "bin" containing the fragment length of the crime sample. Match/binning is a reasonable inferential method in a scientific setting, and in other settings that allow for flexibility, but it has several characteristics that make it undesirable for use in courts. One is that it is based on a yes/no decision: there is an arbitrary cut-off point and some fragments deemed not to match can be arbitrarily close to others that do match. Another is that the same match proportion applies for suspects whose fragment lengths just barely match the lengths of the corresponding fragments in a crime sample as for suspects whose fragment lengths match perfectly. This article describes an alternative approach, one that is not based on a yes/no match criterion. The distribution of a laboratory's measurement errors is used to infer the form of the likelihood function. Then the likelihood ratio of guilt to innocence is calculated and Bayes' theorem is applied. The focus of this approach is the contribution of the DNA evidence to the probability that a suspect is guilty. An important step is estimating the population distribution of fragment lengths, attempting to account for both laboratory measurement error and sampling variability. The two approaches are compared in an actual murder case (New York v. Castro). Applying a laboratory's match criterion literally resulted in an exclusion, but its scientists claimed a match and calculated a match proportion that was very small. Applying Bayes' theorem shows that the correct conclusion is far less clear. DNA profiling is also useful in inferring parentage, for example in cases of disputed paternity. Bayes' theorem allows for calculating the probability that an alleged father is the true father.
"Inferences Using DNA Profiling in Forensic Identification and Paternity Cases." Statist. Sci. 6 (2) 175 - 189, May, 1991. https://doi.org/10.1214/ss/1177011822