A phase-type distribution describes the time to absorption in a continuous- or discrete-time Markov chain. Phase-type distributions have been successfully used in different fields of applied probability. We illustrate how results from phase type theory can be applied to derive properties of the Kingman-coalescent process which is used to model the genealogy of samples of DNA sequences in population genetics. Providing an alternative to previous work based on the Laplace transform, we derive likelihoods for small size coalescent trees based on phase-type theory. Their application towards statistical inference is also explored.

If time permits, we will also briefly discuss further applications in this area.

The talk is based on joint work with Asger Hobolth, Iker Rivas-Gonzalez and Mogens Bladt from Denmark.

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