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Paper No. 12-11

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N Shiers and JQ Smith

Graphical inequality diagnostics for phylogenetic trees

Abstract: Phylogenetic trees can be studied as discrete Bayesian networks with interior vertices hidden and leaves observed. In the case of binary random variables it has long been known that this class of models constrains the parameter space of the leaf margin. However, it was only last year that the inequality constraints were fully characterised for binary phylogenetic trees. The inferential consequences of these implicit inequality constraints have so far attracted little attention. However, this paper uses a subset of these constraints to demonstrate their usefulness as simple and transparent diagnostics that can be used at the preliminary stages of a phylogenetic analysis, not only to check whether any phylogenetic model is consistent with the data but also to guide the ensuing inference.