Phase-type models#
In this section, we present a tutorial for computing and illustrating Phase-Type distributions under the different admixture models implemented in tracts. In tracts 2.0, several new models are introduced with increasing levels of complexity. These models arise as successive simplifications of each other, starting from the so-called pedigree-wide and ancestral-pedigree models presented in the paper, but not implemented due to their high computational complexity.
At each stage of simplification, the state space is reduced by grouping states into super-states, and transitions between these super-states are assumed to be Markovian. In tracts 2.0, we implement the last three stages of this simplification process: the Dioecious-Fine (DF) model, the Dioecious-Coarse (DC) model, and the Monoecious (M) model, the latter of which was already available in tracts 1.0. Note that, unlike the Monoecious model, the Dioecious models introduced in this version allow for modelling admixture on the X chromosome. For further details, we refer the reader to the tracts 2.0 paper.
Once the model is chosen, the corresponding transition probabilities are computed. Then, by setting the states corresponding to the population of interest as absorbing, we obtain a Phase-Type distribution that characterizes tract lengths. In this tutorial, we provide code illustrating how to use the functions in tracts 2.0 to build an admixture model and compute the corresponding Phase-Type densities or histograms.
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