Reciprocal Maximum Likelihood Degrees of Brownian Motion Tree Models

09/24/2020

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We give an explicit formula for the reciprocal maximum likelihood degree of Brownian motion tree models. To achieve this, we connect them to certain toric (or log-linear) models, and express the Brownian motion tree model of an arbitrary tree as a toric fiber product of star tree models.

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Reciprocal Maximum Likelihood Degrees of Brownian Motion Tree Models

Toric invariant theory for maximum likelihood estimation in log-linear models

Maximum Likelihood Estimation for Brownian Motion Tree Models Based on One Sample

Brownian motion tree models are toric

Maximum information divergence from linear and toric models

Ancestral state reconstruction with large numbers of sequences and edge-length estimation

Parameter Redundancy and the Existence of Maximum Likelihood Estimates in Log-linear Models

An Approximation Algorithm for Ancestral Maximum-Likelihood and Phylogeography Inference Problems under Time Reversible Markov Evolutionary Models

Reciprocal Maximum Likelihood Degrees of Brownian Motion Tree Models

Related Research

Toric invariant theory for maximum likelihood estimation in log-linear models

Maximum Likelihood Estimation for Brownian Motion Tree Models Based on One Sample

Brownian motion tree models are toric

Maximum information divergence from linear and toric models

Ancestral state reconstruction with large numbers of sequences and edge-length estimation

Parameter Redundancy and the Existence of Maximum Likelihood Estimates in Log-linear Models

An Approximation Algorithm for Ancestral Maximum-Likelihood and Phylogeography Inference Problems under Time Reversible Markov Evolutionary Models