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

Wai Tong Fan UW-Madison

Information Theory Probability Statistics Theory and Methods mathscidoc:1806.19001

Electronic Journal of Probability, 23, (47), 24, 2018
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].
Markov models on trees; reconstruction problem; concentration inequalities; consistent estimation; information-theoretic bounds; applications to phylogenetics.
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  • https://projecteuclid.org/euclid.ejp/1527213728
@inproceedings{wai2018necessary,
  title={Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees},
  author={Wai Tong Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180619024252534464105},
  booktitle={Electronic Journal of Probability},
  volume={23},
  number={47},
  pages={24},
  year={2018},
}
Wai Tong Fan. Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees. 2018. Vol. 23. In Electronic Journal of Probability. pp.24. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180619024252534464105.
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