Maximum likelihood (ML) estimators for scaled mutation parameters with a strand symmetric mutation model in equilibrium

05/06/2019
by   Claus Vogl, et al.
0

With the multiallelic parent-independent mutation-drift model, the equilibrium proportions of alleles are known to be Dirichlet distributed. A special case is the biallelic model, in which the proportions are beta distributed. A sample taken from these models is then Dirichlet-multinomially or beta-binomially distributed, respectively. Maximum likelihood (ML) estimators for the mutation parameters of the biallelic parent-independent mutation model are available via an expectation maximization algorithm. Assuming small scaled mutation rates, the distribution of a sample of size M can be expanded in a Taylor series of first order. Then the ML estimators for the two parameters in the biallelic model can be expressed using the site frequency spectrum. In this article, we go beyond parent-independent mutation and analyse a strand-symmetric mutation model with six scaled mutation parameters that deviates from parent independent mutation and, generally, from detailed balance. We derive ML estimators for these six parameters assuming mutation-drift equilibrium and small scaled mutation rates. This is the first time that ML estimators are provided for a mutation model more complex than parent-independent mutation.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/03/2021

Estimation of Dirichlet distribution parameters with bias-reducing adjusted score functions

The Dirichlet distribution, also known as multivariate beta, is the most...
research
12/01/2020

The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices

We study multivariate Gaussian models that are described by linear condi...
research
01/13/2021

Multivariate phase-type theory for the site frequency spectrum

Linear functions of the site frequency spectrum (SFS) play a major role ...
research
04/16/2019

Maximizing Drift is Not Optimal for Solving OneMax

It seems very intuitive that for the maximization of the OneMax problem ...
research
07/20/2022

Maximum Likelihood Imputation

Maximum likelihood (ML) estimation is widely used in statistics. The h-l...
research
03/29/2019

Estimation of cell lineage trees by maximum-likelihood phylogenetics

CRISPR technology has enabled large-scale cell lineage tracing for compl...
research
04/30/2020

One-Step Estimation With Scaled Proximal Methods

We study statistical estimators computed using iterative optimization me...

Please sign up or login with your details

Forgot password? Click here to reset