Seeing the wood for the trees: philosophical aspects of classical, Bayesian and likelihood approaches in statistical inference and some implications for phylogenetic analysis

Abstract

The three main approaches in statistical inference—classical statistics, Bayesian and likelihood—are in current use in phylogeny research. The three approaches are discussed and compared, with particular emphasis on theoretical properties illustrated by simple thought-experiments. The methods are problematic on axiomatic grounds (classical statistics), extra-mathematical grounds relating to the use of a prior (Bayesian inference) or practical grounds (likelihood). This essay aims to increase understanding of these limits among those with an interest in phylogeny.