Geodesic
Localizing influential genes with modified versions of Bayesian Information Criterion
Mathematica Applicanda, Tome 40 (2012) no. 1, pp. 3-14.

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Regions of the genome that influence quantitative traits are called quantitative trait loci (QTLs) and can be located using statistical methods. For this aim scientists use genetic markers, whose genotypes are known, and look for the associations between these genotypes and trait values. The common method which can be used in this problem is a linear regression. There are many model selection criteria for the choice of predictors in a linear regression. However, in the context of QTL mapping, where the number of available markers $p_n$ is usually bigger than the sample size $n$, the classical criteria overestimate the number of regressors. To solve this problem several modifications of the {\it Bayesian Information Criterion} have been proposed and it has been recently proved that at least three of them, EBIC, mBIC and mBIC2, are consistent (also in case when $p_n>n$). In this article we discuss these criteria and their asymptotic properties and compare them by an extensive simulation study in the genetic context.
DOI : 10.14708/ma.v40i1.274
Classification : 62J05;92D20
Mots-clés : statistical genetics, quantitative trait loci, model selection, sparse linear regression, Bayesian Information Criterion 
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Małgorzata Bogdan; Piotr Szulc. Localizing influential genes with modified versions of Bayesian Information Criterion. Mathematica Applicanda, Tome 40 (2012) no. 1, pp.  3-14. doi : 10.14708/ma.v40i1.274. http://geodesic.mathdoc.fr/articles/10.14708/ma.v40i1.274/

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