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9. The SgLasso and its cousins for selective genotyping and extreme sampling: application to association studies and genomic selection

Author

Rabier, Charles-Elie, DELMAS, Céline, Institut des Sciences de l'Evolution de Montpellier (UMR ISEM), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-École pratique des hautes études (EPHE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Montpellier (UM)-Institut de recherche pour le développement [IRD] : UR226-Centre National de la Recherche Scientifique (CNRS), Méthodes et Algorithmes pour la Bioinformatique (MAB), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Unité de Mathématiques et Informatique Appliquées de Toulouse (MIAT INRA), Institut National de la Recherche Agronomique (INRA), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-École pratique des hautes études (EPHE)-Université de Montpellier (UM)-Institut de recherche pour le développement [IRD] : UR226-Centre National de la Recherche Scientifique (CNRS), École pratique des hautes études (EPHE), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Institut de recherche pour le développement [IRD] : UR226

Subjects
[SDV.GEN]Life Sciences [q-bio]/Genetics, [SDV]Life Sciences [q-bio], Extremes, High-Dimensional Linear Model, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT]Statistics [stat], [SDV.GEN.GPL]Life Sciences [q-bio]/Genetics/Plants genetics, Genomic Selection, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Variable Selection, Sparsity AMS Subject Classification: Primary 60G15, Linear Model, 62F05, 62F03, Gaussian process, Prediction, Sparsity, Selective Genotyping, [STAT.ME]Statistics [stat]/Methodology [stat.ME], High Dimension
Abstract

International audience; We introduce a new variable selection method, called SgLasso, that handles extreme data, and suitable when the correlation between regressors is known. It is appropriate in genomics since once the genetic map has been built, the correlation is perfectly known. Besides, we prove that the signal to noise ratio is largely increased by considering the extremes. Our method relies on the construction of a specific statistical test, a transformation of the data and by the knowledge of the correlation between regressors. This new technique is inspired by stochastic processes arising from statistical genetics. Our approach and existing methods are compared for simulated and real data, and the results point to the validity of our approach.; . Nous introduisons une nouvelle méthode de selection de variables, nommée SgLasso, qui prend en compte les données extrêmes. Notre méthode est basée sur la construction d'un test statistique spécifique, une transformation des données et par la connaissance de la corrélation entre régresseurs. Cela s'avère approprié en génomique car une fois la carte génétique construite, cette corrélation est parfaitement connue. Cette nouvelle technique est inspirée des processus stochastiques en provenance de la statistique génétique. Nous prouvons que le rapport signal bruit est largement augmenté en considérant les extrêmes. Notre approche ainsi que les méthodes existantes sont comparées sur données simulées et réelles. Ceci valide notre nouvelle approche.

Published
2020

10. On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo

Author

Rabier, Charles-Elie, Berry, Vinvent, Stoltz, Marnus, Santos, João D., Wang, Wensheng, Glaszmann, Jean-Christophe, Pardi, Fabio, Scornavacca, Céline, Rabier, Charles-Elie, Berry, Vinvent, Stoltz, Marnus, Santos, João D., Wang, Wensheng, Glaszmann, Jean-Christophe, Pardi, Fabio, and Scornavacca, Céline

Abstract

For various species, high quality sequences and complete genomes are nowadays available for many individuals. This makes data analysis challenging, as methods need not only to be accurate, but also time efficient given the tremendous amount of data to process. In this article, we introduce an efficient method to infer the evolutionary history of individuals under the multispecies coalescent model in networks (MSNC). Phylogenetic networks are an extension of phylogenetic trees that can contain reticulate nodes, which allow to model complex biological events such as horizontal gene transfer, hybridization and introgression. We present a novel way to compute the likelihood of biallelic markers sampled along genomes whose evolution involved such events. This likelihood computation is at the heart of a Bayesian network inference method called SnappNet, as it extends the Snapp method inferring evolutionary trees under the multispecies coalescent model, to networks. SnappNet is available as a package of the well-known beast 2 software. Recently, the MCMC_BiMarkers method, implemented in PhyloNet, also extended Snapp to networks. Both methods take biallelic markers as input, rely on the same model of evolution and sample networks in a Bayesian framework, though using different methods for computing priors. However, SnappNet relies on algorithms that are exponentially more time-efficient on non-trivial networks. Using simulations, we compare performances of SnappNet and MCMC_BiMarkers. We show that both methods enjoy similar abilities to recover simple networks, but SnappNet is more accurate than MCMC_BiMarkers on more complex network scenarios. Also, on complex networks, SnappNet is found to be extremely faster than MCMC_BiMarkers in terms of time required for the likelihood computation. We finally illustrate SnappNet performances on a rice data set. SnappNet infers a scenario that is consistent with previous results and provides additional understanding of rice evolution.

Published
2021

13. On the accuracy in high dimensional linear models under imperfect linkage disequilibrium

Author

Rabier , Charles-Elie, Grusea , Simona, Institut des Sciences de l'Evolution de Montpellier (UMR ISEM), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (CIRAD)-École pratique des hautes études (EPHE)-Université de Montpellier (UM)-Institut de recherche pour le développement [IRD] : UR226-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Toulouse-Université Toulouse III - Paul Sabatier (UPS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Institut des Sciences de l'Evolution de Montpellier ( UMR ISEM ), Centre de Coopération Internationale en Recherche Agronomique pour le Développement ( CIRAD ) -Université de Montpellier ( UM ) -Institut de recherche pour le développement [IRD] : UR226-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier ( LIRMM ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), and Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
Genomic Selection, Ridge Regression, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Linear Model, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], Singular Value Decomposition, Prediction, Sparsity, Accuracy, High Dimension
Abstract

Genomic selection (GS) consists in predicting breeding values of selection candidates, using a large number of genetic markers. An important question in GS is the determination of the number of markers required for a good prediction. Many studies show that it becomes useless to consider too many markers. In contrast, for some species, the number of markers remains too small to cover the huge genome size. Under such sparse genetic map, it is likely to observe some imperfect linkage disequilibrium: the alleles at a gene location and at a marker located nearby vary. In this context, we tackle here the problem of imperfect linkage disequilibrium in the Ridge regression framework. We present theoretical results regarding the accuracy criteria, i.e., the correlation between predicted value and true value. We show the influence of the projection of the causal regression function (i.e. at genes) on the space spanned by the columns of the design matrix (i.e. at markers). Asymptotic results, in a high dimensional framework, are given, and we prove that the convergence to an optimal accuracy depends on a few limiting factors. This study generalizes our recent results (Rabier et al. (2018)) obtained under perfect linkage disequi-librium. Last, illustrations on simulated and real data are proposed.

Published
2019

14. Training set optimization of genomic prediction by means of EthAcc

Author

Mangin, Brigitte, Rincent, Renaud, Rabier, Charles-Elie, Moreau, Laurence, Goudemand-Dugue, Ellen, Laboratoire des interactions plantes micro-organismes (LIPM), Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS), Génétique Diversité et Ecophysiologie des Céréales (GDEC), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Institut National de la Recherche Agronomique (INRA), Université de Montpellier (UM), Institut des Sciences de l'Evolution de Montpellier (UMR ISEM), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-École pratique des hautes études (EPHE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Montpellier (UM)-Institut de recherche pour le développement [IRD] : UR226-Centre National de la Recherche Scientifique (CNRS), Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale) (GQE-Le Moulon), Centre National de la Recherche Scientifique (CNRS)-AgroParisTech-Université Paris-Sud - Paris 11 (UP11)-Institut National de la Recherche Agronomique (INRA), Florimond Desprez, French National Research Agency (ANR) : ANR-11-BTBR-0007, ANR-10-BTBR-03, ANR-11-BTBR-0005, Institut National de la Recherche Agronomique (INRA)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020]), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-École Pratique des Hautes Études (EPHE), and Institut National de la Recherche Agronomique (INRA)-Université Paris-Sud - Paris 11 (UP11)-AgroParisTech-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SDV]Life Sciences [q-bio], Plant Science, Plant Genetics, Mathematical and Statistical Techniques, Plant Genomics, Triticum, Genome, Applied Mathematics, Simulation and Modeling, Eukaryota, Genomics, Plants, Chemistry, Phenotype, [SDE]Environmental Sciences, Physical Sciences, Wheat, Medicine, Engineering and Technology, Helianthus, Beta vulgaris, Algorithms, Research Article, Biotechnology, Chemical Elements, Optimization, Genotype, Science, Quantitative Trait Loci, Bioengineering, Research and Analysis Methods, Zea mays, Genetics, Genome-Wide Association Studies, [SDV.BV]Life Sciences [q-bio]/Vegetal Biology, Computer Simulation, Grasses, Models, Genetic, Sodium, Organisms, Biology and Life Sciences, Computational Biology, Human Genetics, Genome Analysis, Plant Breeding, Genetic Loci, Plant Biotechnology, Mathematical Functions, Mathematics, Genome-Wide Association Study
Abstract

International audience; Genomic prediction is a useful tool for plant and animal breeding programs and is starting to be used to predict human diseases as well. A shortcoming that slows down the genomic selection deployment is that the accuracy of the prediction is not known a priori. We propose EthAcc (Estimated THeoretical ACCuracy) as a method for estimating the accuracy given a training set that is genotyped and phenotyped. EthAcc is based on a causal quantitative trait loci model estimated by a genome-wide association study. This estimated causal model is crucial; therefore, we compared different methods to find the one yielding the best EthAcc. The multilocus mixed model was found to perform the best. We compared EthAcc to accuracy estimators that can be derived via a mixed marker model. We showed that EthAcc is the only approach to correctly estimate the accuracy. Moreover, in case of a structured population, in accordance with the achieved accuracy, EthAcc showed that the biggest training set is not always better than a smaller and closer training set. We then performed training set optimization with EthAcc and compared it to CDmean. EthAcc outperformed CDmean on real datasets from sugar beet, maize, and wheat. Nonetheless, its performance was mainly due to the use of an optimal but inaccessible set as a start of the optimization algorithm. EthAcc's precision and algorithm issues prevent it from reaching a good training set with a random start. Despite this drawback, we demonstrated that a substantial gain in accuracy can be obtained by performing training set optimization.

Published
2019
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15. On gene mapping with the mixture model and the extremes

Author

Rabier, Charles-Elie, DELMAS, Céline, Institut des Sciences de l'Evolution de Montpellier (UMR ISEM), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-École Pratique des Hautes Études (EPHE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Montpellier (UM)-Institut de recherche pour le développement [IRD] : UR226-Centre National de la Recherche Scientifique (CNRS), Unité de Mathématiques et Informatique Appliquées de Toulouse (MIAT INRA), Institut National de la Recherche Agronomique (INRA), Méthodes et Algorithmes pour la Bioinformatique (MAB), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-École pratique des hautes études (EPHE)-Université de Montpellier (UM)-Institut de recherche pour le développement [IRD] : UR226-Centre National de la Recherche Scientifique (CNRS), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-École pratique des hautes études (EPHE), and Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)

Subjects
Mixture model, Hypothesis testing, Extreme values, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Quantitative Trait Locus detection, Gaussian process, Selective genotyping, Quantitative Trait Locus de-tection
Abstract

We introduce a new variable selection method, suitable when the correlation between regressors is known. It is appropriate in genomics since once the genetic map has been built, the correlation is perfectly known. Our method, based on the LASSO , is original since the number of selected variables is bounded by the number of predictors, instead of being bounded by the number of observations as in the classical LASSO. It is made possible by the construction of a specific statistical test, a transformation of the data and by the knowledge of the correlation between regressors. We prove that the signal to noise ratio is largely increased by considering the extremes. This new technique is inspired by stochastic processes arising from statistical genetics. It is described in a statistical genetics context, considering a large panel of models present in the literature. Our method is insensitive to interactions between regressors. An illustration on simulated data is given.

Published
2018

19. On Quantitative Trait Locus mapping with an interference phenomenom

Author

Rabier, Charles-Elie, Station d'Amélioration Génétique des Animaux (SAGA), Institut National de la Recherche Agronomique (INRA), Laboratoire de Statistique et Probabilités (LSP), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Nuisance parameters present only under the alternative, MCQMC, Likelihood Ratio Test, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Gaussian process, Mixture models, QTL detection
Abstract

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval $[0,T]$ representing a chromosome. The observation is the trait and the composition of the genome at some locations called ''markers''. As in Rebai et al. (95), we focus on the interference phenomenom : a recombination event inhibes the formation of another nearby. We give the asymptotic distribution of the LRT process under the null hypothesis that there is no QTL on $[0,T]$ and under local alternatives with a QTL at $t^{\star}$ on $[0,T]$. We show that the LRT process is asymptotically the square of a ''linear interpolated and normalized process '' whereas the LRT process obtained recently by Azais et al., for a model without interference, was the square of a ''non linear interpolated and normalized process ''. The computation of the supremum of our LRT process becomes easy due to the interpolation. Besides, we proove that the MCQMC method to compute thresholds for QTL detection, proposed by Azais et al., is still suitable for our model with interference.

Published
2012

20. On interpolations in QTL detection

Author

Delmas, Céline, Rabier, Charles-Elie, Station d'Amélioration Génétique des Animaux (SAGA), Institut National de la Recherche Agronomique (INRA), Laboratoire de Statistique et Probabilités (LSP), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Nuisance parameters present only under the alternative, Likelihood Ratio Test, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Gaussian process, Mixture models, QTL detection
Abstract

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0,T] representing a chromosome. Recently, Azais et al. proved that the LRT process was the square of a non linear interpolated process. However, in their study of the same problem, Chang et al. introduced another interpolation. So, why do Azais and Chang find different interpolations ? We correct errors present in the interpolation of Chang and establish the link between the two interpolations. We finally generalize the interpolation of Chang to the alternative hypothesis of a QTL located at t* inside [0,T].

Published
2012

21. Threshold and power for Quantitative Trait Locus detection

Author

Rabier, Charles-Elie, Azaïs, Jean-Marc, Elsen, Jean-Michel, DELMAS, Céline, Station d'Amélioration Génétique des Animaux (SAGA), Institut National de la Recherche Agronomique (INRA), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), SABRE, CNRS, Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Chi-Square process, Multiple Testing, Likelihood Ratio Test, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Threshold, Monte-Carlo methods, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Quantitative Biology::Genomics, QTL detection
Abstract

We propose several new methods to calculate threshold and power for Quantitative Trait Locus (QTL) detection. They are based on asymptotic theoretical results presented in Rabier et al. (2009) . The asymptotic validity is checked by simulations. The methods proposed are fast and easy to implement. A comparison of power between a multiple testing procedure and a global test has been realized, showing far better performances of the global test for the detection of a QTL.

Published
2010

22. Techniques statistiques pour la détection de gènes à effets quantitatifs

Author

Rabier, Charles-Elie, ProdInra, Migration, Station d'Amélioration Génétique des Animaux (SAGA), Institut National de la Recherche Agronomique (INRA), Université Toulouse III - Paul Sabatier, Jean-Marc AZAIS, and Jean-Michel ELSEN

Subjects
[SDV] Life Sciences [q-bio], MODELES DE MELANGE, QTL, MONTE CARLO QUASI MONTE CARLO, [SDV]Life Sciences [q-bio], MODELES STATISTIQUES A PARAMETRES DE NUISANCE, PROCESSUS DE CHI-DEUX, PROCESSUS GAUSSIEN
Abstract

Diplôme : Fin d'études

Published
2010

23. Likelihood Ratio Test process for Quantitative Trait Loci detection

Author

Rabier, Charles-Elie, Azaïs, Jean-Marc, Delmas, Céline, Station d'Amélioration Génétique des Animaux (SAGA), Institut National de la Recherche Agronomique (INRA), Laboratoire de Statistique et Probabilités (LSP), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), SABRE, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Nuisance parameters present only under the alternative, Likelihood Ratio Test, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], chi-square process, food and beverages, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Gaussian process, Mixture models, QTL detection
Abstract

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL on the interval [0,T] representing a chromosome (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait). We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0,T] and under the general alternative that there exist m QTL on [0,T]. We propose to estimate the number of QTL, their positions and their effects by penalized likelihood. Our results are extended to the case where individuals are structured into families.

Published
2009

24. Selective genotyping pour la détection de QTL

Author

Rabier, Charles-Elie, Azais, Jean-Marc, LSP (LSP), Institut National de la Recherche Agronomique (INRA), Laboratoire de Statistique et Probabilités (LSP), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
Abstract

International audience; Les nouvelles technologies en matière de génomique se révèlent être efficaces afin de percer les secrets de la variation génétique d'un caractère quantitatif. Ces technologies permettent la caractérisation moléculaire de marqueurs polymorphes (i.e. présentant plusieurs allèles) sur l'ensemble du génome. Ces derniers seront par la suite utilisés pour identifier et localiser les loci (i.e. emplacements physiques précis sur un chromosome) où la variation allélique est associée à la variation du caractère quantitatif considéré. On nomme QTL de tels loci. Néanmoins, les coûts dûs au génotypage demeurent très élevés. C'est pourquoi l'optimisation du processus expérimental est primordiale. L'un de ces processus expérimentaux s'intitule selective genotyping. Il a été proposé par Lebowitz and al. (1987), et élaboré par Lander et Botstein (1989), Darvasi et Soller (1992), Muranty et Goffinet (1997). Le selective genotyping consiste à génotyper uniquement les individus dont la valeur du caractère quantitatif est extrême (plus grande ou plus petite qu'un seuil). Cela permet de réduire les coûts dûs au génotypage tout en gardant une bonne puissance pour le test statistique, à condition que le nombre d'individus ait été augmenté. Dans cet exposé, sont étudiées différentes stratégies pour l'analyse statistique en selective genotyping. Les tests statistiques correspondants, seront comparés en terme d'efficacité au test oracle, celui où tous les génotypes sont connus.

Published
2009

25. Asymptotic distribution of the likelihood ratio test in QTL detection

Author

Rabier, Charles-Elie, DELMAS, Céline, Elsen, Jean Michel, Station d'Amélioration Génétique des Animaux (SAGA), and Institut National de la Recherche Agronomique (INRA)

Subjects
LIKELIHOOD, RATIO, MARKERS, CHROMOSOME, QTL, [SDV]Life Sciences [q-bio], ComputingMilieux_MISCELLANEOUS, THRESHOLD
Abstract

International audience

Published
2008

33. On stochastic processes for quantitative trait locus mapping under selective genotyping.

Author

Rabier, Charles-Elie

Subjects
*STOCHASTIC processes, *QUANTITATIVE research, *LIKELIHOOD ratio tests, *CHROMOSOMES, *PROBABILITY theory, *GAUSSIAN processes
Abstract

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0,T] representing a chromosome. The originality of this study is that we are under selective genotyping: only the individuals with extreme phenotypes are genotyped. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0,T] and under local alternatives with a QTL att☆on [0,T]. We show that the LRT process is asymptotically the square of a ‘non-linear interpolated and normalized Gaussian process’. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that we have to genotype symmetrically and that the threshold is exactly the same as in the situation where all the individuals are genotyped. [ABSTRACT FROM AUTHOR]

Published
2015
Full Text
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34. Likelihood ratio test process for quantitative trait locus detection.

Author

Azaïs, Jean-Marc, Delmas, Céline, and Rabier, Charles-Elie

Subjects
LIKELIHOOD ratio tests, QUANTITATIVE research, CHROMOSOMES, LOCUS (Genetics), GAUSSIAN processes, MATHEMATICAL models, PARAMETER estimation
Abstract

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0,T], representing a chromosome. The observation is the trait and the composition of the genome at some locations called ‘markers’. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0,T] and under local alternatives with a QTL att☆on [0,T]. We show that the LRT is asymptotically the square of some Gaussian process. We give a description of this process as an ‘non-linear interpolated and normalized process’. We propose a simple method to calculate the maximum of the LRT process using only statistics on markers and their ratio. This gives a new method to calculate thresholds for the QTL detection. [ABSTRACT FROM PUBLISHER]

Published
2014
Full Text
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