Enclosing the Maximum Likelihood of the Simplest DNA Model Evolving on Fixed Topologies: Towards a Rigorous Framework for Phylogenetic Inference
Raazesh Sainudiin · 2004
An interval extension of the recursive formulation for the likelihood function of the simplest Markov model of DNA evolution on unrooted phylogenetic trees with a fixed topology is used to obtain rigorous enclosure(s) of the global maximum likelihood. Validated global maximizer(s) inside any compact set of the parameter space which is the set of all branch lengths of the tree are thus obtained. The algorithm is an adaptation of a widely applied global optimization method using interval analysis for the phylogenetic context. The method is applied to enclose the maximizer(s) and the global maximum for the simplest DNA model evolving on trees with 2, 3, and 4 taxa. The method is also applicable to a wide class of inclusion isotonic likelihood functions.