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Abstract
We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate matrix follows the model structure. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric groupbased phylogenetic models. In particular, we provide necessary and sufficient conditions in terms of the eigenvalues of symmetric groupbased matrices. To showcase our main result on model embeddability, we provide an application to hachimoji models, which are eightstate models for synthetic DNA. Moreover, our main result on model embeddability enables us to compute the volume of the set of model embeddable Markov matrices relative to the volume of other relevant sets of Markov matrices within the model.
Original language  English 

Article number  33 
Number of pages  26 
Journal  Journal of Mathematical Biology 
Volume  83 
Issue number  3 
DOIs  
Publication status  Published  9 Sep 2021 
MoE publication type  A1 Journal articlerefereed 
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Algebraic geometry of hidden variable models in statistics
Kuznetsova, O., Kubjas, K. & Sodomaco, L.
01/09/2019 → 31/08/2023
Project: Academy of Finland: Other research funding