Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees
- Resource Type
- Working Paper
- Authors
- Fan, Wai-Tong Louis; Roch, Sebastien
- Source
- Electronic Journal of Probability, Vol. 23 (47), 1-24, 2018
- Subject
- Mathematics - Probability
Computer Science - Information Theory
Mathematics - Statistics Theory
Quantitative Biology - Populations and Evolution
60J25, 60J80, 62B10, 62M05
- Language
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.
Comment: 30 pages, 3 figures, title of reference [FR] is updated