Maximum likelihood with multiparameter models of substitution |
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Authors: | Elisabeth Renée Marie Tillier |
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Institution: | (1) Department of Botany, University of Toronto, M5S 3B2 Toronto, Ontario, Canada;(2) Present address: New York State Department of Health, Wadsworth Center for Laboratories and Research, David Axelrod Institute, PO Box 22002, 12201-2002 Albany, NY, USA |
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Abstract: | Maximum-likelihood approaches to phylogenetic estimation have the potential of great flexibility, even though current implementations are highly constrained. One such constraint has been the limitation to one-parameter models of substitution. A general implementation of Newton's maximization procedure was developed that allows the maximum likelihood method to be used with multiparameter models. The Estimate and Maximize (EM) algorithm was also used to obtain a good approximation to the maximum likelihood for a certain class of multiparameter models. The condition for which a multiparameter model will only have a single maximum on the likelihood surface was identified. Two-and three-parameter models of substitution in base-paired regions of RNA sequences were used as examples for computer simulations to show that these implementations of the maximum likelihood method are not substantially slower than one-parameter models. Newton's method is much faster than the EM method but may be subject to divergence in some circumstances. In these cases the EM method can be used to restore convergence. |
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Keywords: | Maximum likelihood Likelihood point Evolutionary models Maximization algorithms Evolution in base-paired RNA |
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