@TechReport{ it:2002-005,
author = {Kajsa Ljungberg and Sverker Holmgren and {\"O}rjan
Carlborg},
title = {Efficient Kernel Algorithms for QTL Mapping Problems},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2002},
number = {2002-005},
month = feb,
abstract = {The advent of sophisticated and powerful methods for
molecular genetics pushes the need for efficient methods
for data analysis. Advanced algorithms are necessary for
extracting all possible information from laboriously
obtained data sets. We present a general linear algebra
framework for QTL mapping, applicable to many commonly used
methods, using both linear regression and maximum
likelihood estimation. The formulation simplifies future
comparisons between and analyses of the methods. We show
how the common structure of QTL analysis models can be used
to improve the kernel algorithms, drastically reducing the
computational effort while retaining the original analysis
results. We have evaluated our new algorithms on data sets
originating from two large F$_2$ populations of domestic
animals. Using an updating approach, we show that 1-3
orders of magnitude reduction in computational demand can
be achieved for matrix factorizations. For interval
mapping/composite interval mapping settings using a maximum
likelihood model, we also show how to use the original EM
algorithm instead of the ECM approximation, significantly
improving the convergence and introducing an additional
reduction in the computational time. The algorithmic
improvements makes it feasible to perform analyses
previously deemed impractical or even impossible. For
example, using the new algorithms it is reasonable to
perform permutation testing using exhaustive search on
populations of 200 individuals for fully epistatic two-QTL
models with a large number of parameters. }
}