The genealogy of multi-type branching processes

Context: Multilevel splitting, an algorithm used for rare events simulation, can be modelled as a discrete-time multi-type branching process.

Aims: This project explores the expected genealogy of terminal trajectories, with a focus on being able to numerically estimate probabilities related to coalescence. We research how ideas from statistical genetics can help tune the parameters of the multilevel splitting algorithm, such as the numer of levels or the offspring distribution.

Novelty: The results about genealogies of this type of branching processes are scarce and do not tend to consider numerical evaluation.