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2018 Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees
Wai-Tong (Louis) Fan, Sebastien Roch
Electron. J. Probab. 23: 1-24 (2018). DOI: 10.1214/18-EJP165

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 [GS10] and have implications for ancestral sequence reconstruction in a classical evolutionary model of nucleotide insertion and deletion [TKF91].

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Wai-Tong (Louis) Fan. Sebastien Roch. "Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees." Electron. J. Probab. 23 1 - 24, 2018. https://doi.org/10.1214/18-EJP165

Information

Received: 16 July 2017; Accepted: 4 April 2018; Published: 2018
First available in Project Euclid: 25 May 2018

zbMATH: 06924659
MathSciNet: MR3814241
Digital Object Identifier: 10.1214/18-EJP165

Subjects:
Primary: 60J25 , 60J80 , 62B10 , 62M05

Keywords: applications to phylogenetics , Concentration inequalities , consistent estimation , information-theoretic bounds , Markov models on trees , reconstruction problem

JOURNAL ARTICLE
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