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

Wai-Tong Louis Fan; Sebastien Roch

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arXiv · 1707.05702

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

Wai-Tong Louis Fan·Sebastien Roch

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Abstract

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 sequence reconstruction in a classical evolutionary model of nucleotide insertion and deletion.

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BibTeX RIS

Wai-Tong Louis Fan, Sebastien Roch. 2017-07-18. Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees. https://arxiv.org/abs/1707.05702

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