Phase transition on the convergence rate of parameter estimation under an Ornstein-Uhlenbeck diffusion on a tree

DOI10.1007/s00285-016-1029-xzbMath1358.62069arXiv1406.1568OpenAlexW2963318278WikidataQ39724564 ScholiaQ39724564MaRDI QIDQ504087

Sebastien Roch, Cécile Ané, Lam Si Tung Ho

Publication date: 25 January 2017

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.1568

zbMATH Keywords

consistencyphase transitionmaximum likelihood estimatorevolutionOrnstein-Uhlenbeckphylogenetic

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Applications of statistics to biology and medical sciences; meta analysis (62P10) Non-Markovian processes: estimation (62M09) Problems related to evolution (92D15) Taxonomy, cladistics, statistics in mathematical biology (92B10) Diffusion processes (60J60)

Related Items (9)

When can we reconstruct the ancestral state? Beyond Brownian motion ⋮ When can we reconstruct the ancestral state? A unified theory ⋮ Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations ⋮ A parametric interpretation of Bayesian nonparametric inference from gene genealogies: linking ecological, population genetics and evolutionary processes ⋮ Phylogenetic confidence intervals for the optimal trait value ⋮ On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model ⋮ A Central Limit Theorem for punctuated equilibrium ⋮ Species tree estimation under joint modeling of coalescence and duplication: sample complexity of quartet methods ⋮ Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

Uses Software

• ape
• GEIGER

Cites Work

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• A phylogenetic comparative method for studying multivariate adaptation
• Asymptotic theory with hierarchical autocorrelation: Ornstein-Uhlenbeck tree models
• \(U\)-statistics of Ornstein-Uhlenbeck branching particle system
• Majority rule has transition ratio 4 on Yule trees under a 2-state symmetric model
• Functionals of critical multitype branching processes
• Broadcasting on trees and the Ising model.
• CLT for Ornstein-Uhlenbeck branching particle system
• Phylogenetic confidence intervals for the optimal trait value
• Mathematical Statistics
• Robust Estimation of Latent Tree Graphical Models: Inferring Hidden States With Inexact Parameters

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