mdh.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
New Algorithms for Evaluating the Log-likelihood Function Derivatives in the AI-REML Method
Mälardalen University, School of Education, Culture and Communication.
Uppsala University.
2009 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 38, no 6, p. 1348-1364Article in journal (Refereed) Published
Abstract [en]

 In this study, we propose several improvements of the Average Information Restricted Maximum Likelihood algorithms for estimating the variance components for genetic mapping of quantitative traits. The improved methods are applicable when two variance components are to be estimated. The improvements are related to the algebraic part of the methods and utilize the properties of the underlying matrix structures. In contrast to previously developed algorithms, the explicit computation of a matrix inverse is replaced by the solution of a linear system of equations with multiple right-hand sides, based on a particular matrix decomposition. The computational costs of the proposed algorithms are analyzed and compared.

Place, publisher, year, edition, pages
2009. Vol. 38, no 6, p. 1348-1364
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:mdh:diva-4222DOI: 10.1080/03610910902912944ISI: 000270912200008Scopus ID: 2-s2.0-70449641719OAI: oai:DiVA.org:mdh-4222DiVA, id: diva2:121263
Available from: 2008-04-28 Created: 2008-04-28 Last updated: 2017-12-14Bibliographically 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

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus
By organisation
School of Education, Culture and Communication
In the same journal
Communications in statistics. Simulation and computation
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 63 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf