Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees [article]

Wai-Tong Louis Fan, Sebastien Roch
2019 arXiv   pre-print
We establish necessary and sufficient conditions for consistent root reconstruction in continuous-time Markov models with countable state space on bounded-height trees. Here a root state estimator is said to be consistent if the probability that it returns to the true root state converges to 1 as the number of leaves tends to infinity. We also derive quantitative bounds on the error of reconstruction. Our results answer a question of Gascuel and Steel and have implications for ancestral
more » ... reconstruction in a classical evolutionary model of nucleotide insertion and deletion.
arXiv:1707.05702v3 fatcat:dgzjjjr7xja7jlzvxla7wi5qhe