Thore Egeland: Markov models for mutations

Title: Markov models for mutations Abstract: The talk is motivated by forensic genetics generally and paternity cases specifically. There are roughly 2000 paternity cases in Norway every year. The generic hypotheses are H1: "Peder Ås is the father of Lars" and H2: "An unknown, unrelated man is the father of Lars". A likelihood ratio LR=L(H1)/L(H2) is calculated to assess the strength of the evidence. Mutations occur in roughly 1% of the cases and leads to a LR of 0 and rejecting H1 unless mutations are modelled. It is therefore important to accommodate mutations and this is typically done using discrete markov chains to model transitions from parent to child. In this talk I will discuss recent developments and the relevance of stationarity and detailed balance (reversibility) of markov chains and the implications for applications like the one mentioned above.