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

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.