Hessian Calculation for Phylogenetic Likelihood based on the Pruning Algorithm and its Applications
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Toby Kenney
Abstract
We analytically derive the first and second derivatives of the likelihood in maximum likelihood methods for phylogeny. These results enable the Newton-Raphson method to be used for maximising likelihood, which is important because there is a need for faster methods for optimisation of parameters in maximum likelihood methods. Furthermore, the calculation of the Hessian matrix also opens up possibilities for standard likelihood theory to be applied, for inference in phylogeny and for model selection problems. Another application of the Hessian matrix is local influence analysis, which can be used for detecting a number of biologically interesting phenomena. The pruning algorithm has been used to speed up computation of likelihoods for a tree. We explain how it can be used to speed up the computation for the first and second derivatives of the likelihood with respect to branch lengths and other parameters. The results in this paper apply not only to bifurcating trees, but also to general multifurcating trees. We demonstrate the use of our Hessian calculation for the three applications listed above, and compare with existing methods for those applications.
©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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- A New Explained-Variance Based Genetic Risk Score for Predictive Modeling of Disease Risk
- Hessian Calculation for Phylogenetic Likelihood based on the Pruning Algorithm and its Applications
- Cluster-Localized Sparse Logistic Regression for SNP Data
- How to analyze many contingency tables simultaneously in genetic association studies
- Incorporating the Empirical Null Hypothesis into the Benjamini-Hochberg Procedure
- Estimating the Number of One-step Beneficial Mutations
- Testing clonality of three and more tumors using their loss of heterozygosity profiles
- Correction for Founder Effects in Host-Viral Association Studies via Principal Components
- A Non-Homogeneous Dynamic Bayesian Network with Sequentially Coupled Interaction Parameters for Applications in Systems and Synthetic Biology
- An Integrated Hierarchical Bayesian Model for Multivariate eQTL Mapping
- A Novel and Fast Normalization Method for High-Density Arrays
- Performance of MAX Test and Degree of Dominance Index in Predicting the Mode of Inheritance
- A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data
- QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function
- Computing Posterior Probabilities for Score-based Alignments Using ppALIGN
Artikel in diesem Heft
- Article
- A New Explained-Variance Based Genetic Risk Score for Predictive Modeling of Disease Risk
- Hessian Calculation for Phylogenetic Likelihood based on the Pruning Algorithm and its Applications
- Cluster-Localized Sparse Logistic Regression for SNP Data
- How to analyze many contingency tables simultaneously in genetic association studies
- Incorporating the Empirical Null Hypothesis into the Benjamini-Hochberg Procedure
- Estimating the Number of One-step Beneficial Mutations
- Testing clonality of three and more tumors using their loss of heterozygosity profiles
- Correction for Founder Effects in Host-Viral Association Studies via Principal Components
- A Non-Homogeneous Dynamic Bayesian Network with Sequentially Coupled Interaction Parameters for Applications in Systems and Synthetic Biology
- An Integrated Hierarchical Bayesian Model for Multivariate eQTL Mapping
- A Novel and Fast Normalization Method for High-Density Arrays
- Performance of MAX Test and Degree of Dominance Index in Predicting the Mode of Inheritance
- A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data
- QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function
- Computing Posterior Probabilities for Score-based Alignments Using ppALIGN
