Exact Expressions for the Log-likelihood's Hessian in Multivariate Continuous-Time Continuous-Trait Gaussian Evolution along a Phylogeny

Abstract

We presents the closed form formulae for the likelihood Hessian matrix of a family of multivariate continuous-trait Gaussian Markov trait evolution model along a given phylogeny, in which the trait vector's mean is an affine function of that of its ancestor and the variance is not dependent of the trait. Accompanied with this work is an R package called 'glinvci', publicly available on The Comprehensive R Archive Network (CRAN), that can compute Hessian-based approximate confidence regions for these models while at the same time allowing users to have missing data, lost traits, and multiple evolutionary regimes.