Methodology for inferring directed graphs representing generative processes

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In genetics, we observe DNA data which represents the hidden history of populations. This history includes splits and merges of ancient populations. In mathematics, we can model the demographic changes as a generative process and therefore generate a directed graph. Our project is to use the DNA data (SNP data, Identity by descent, etc.) to infer the true history in a statistical Bayesian manner, which relates to both mathematical biology and mathematical sciences.