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Efficient Implementation of the AI-REML Iteration for Variance Component QTL Analysis
Mälardalen University, Department of Mathematics and Physics.
(English)In: Computational Statistics and Data Analysis, ISSN 0167-9473Article in journal (Refereed) Submitted
Identifiers
URN: urn:nbn:se:mdh:diva-4221OAI: oai:DiVA.org:mdh-4221DiVA, id: diva2:121262
Available from: 2008-04-28 Created: 2008-04-28 Last updated: 2015-07-08Bibliographically approved
In thesis
1. Numerical Algorithms for Optimization Problems in Genetical Analysis
Open this publication in new window or tab >>Numerical Algorithms for Optimization Problems in Genetical Analysis
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The focus of this thesis is on numerical algorithms for efficient solution of QTL analysis problem in genetics.

Firstly, we consider QTL mapping problems where a standard least-squares model is used for computing the model fit. We develop optimization methods for the local problems in a hybrid global-local optimization scheme for determining the optimal set of QTL locations. Here, the local problems have constant bound constraints and may be non-convex and/or flat in one or more directions. We propose an enhanced quasi-Newton method and also implement several schemes for constrained optimization. The algorithms are adopted to the QTL optimization problems. We show that it is possible to use the new schemes to solve problems with up to 6 QTLs efficiently and accurately, and that the work is reduced with up to two orders magnitude compared to using only global optimization.

Secondly, we study numerical methods for QTL mapping where variance component estimation and a REML model is used. This results in a non-linear optimization problem for computing the model fit in each set of QTL locations. Here, we compare different optimization schemes and adopt them for the specifics of the problem. The results show that our version of the active set method is efficient and robust, which is not the case for methods used earlier. We also study the matrix operations performed inside the optimization loop, and develop more efficient algorithms for the REML computations. We develop a scheme for reducing the number of objective function evaluations, and we accelerate the computations of the derivatives of the log-likelihood by introducing an efficient scheme for computing the inverse of the variance-covariance matrix and other components of the derivatives of the log-likelihood.

Place, publisher, year, edition, pages
Västerås: Mälardalens högskola, 2008
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 59
Keywords
Quantitative Trait Loci (QTL), restricted maximum likelihood (REML), variance components, average information (AI) matrix, Local optimization, Quasi-Newton method, Active Set method, Hessian approximation, BFGS update
National Category
Computational Mathematics
Research subject
Matematik/tillämpad matematik
Identifiers
urn:nbn:se:mdh:diva-650 (URN)978-91-85485-84-0 (ISBN)
Public defence
2008-06-05, Kappa, U, Högskoleplan 1, Västerås, 13:00
Opponent
Supervisors
Available from: 2008-04-28 Created: 2008-04-28

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