On inferring presence of an individual in a mixture: a Bayesian approach

Homer and others (2008. Resolving individuals contributing trace amounts of DNA to highly complex mixtures using high-density SNP genotyping microarrays. PLoS Genetics 4, e1000167) recently showed that, given allele frequency data for a large number of single nucleotide polymorphisms in a sample together with corresponding population "reference" frequencies, by typing an individual's DNA sample at the same set of loci it can be inferred whether or not the individual was a member of the sample. This observation has been responsible for precautionary removal of large amounts of summary data from public access. This and further work on the problem has followed a frequentist approach. This paper sets out a Bayesian analysis of this problem which clarifies the role of the reference frequencies and allows incorporation of prior probabilities of the individual's membership in the sample.