Academic literature on the topic 'Priors spike-and-slab'

Les modèles à effets mixtes analysent des observations collectées de façon répétée sur plusieurs individus, attribuant la variabilité à différentes sources (intra-individuelle, inter-individuelle, résiduelle). Prendre en compte cette variabilité est essentiel pour caractériser sans biais les mécanismes biologiques sous-jacents. Ces modèles utilisent des covariables et des effets aléatoires pour décrire la variabilité entre individus : les covariables décrivent les différences dues à des caractéristiques observées, tandis que les effets aléatoires représentent la variabilité non attribuable aux covariables mesurées. Dans un contexte de grande dimension, où le nombre de covariables dépasse celui des individus, identifier les covariables influentes est difficile, car la sélection porte sur des variables latentes du modèle. De nombreuses procédures ont été mises au point pour les modèles linéaires à effets mixtes, mais les contributions pour les modèles non-linéaires sont rares et manquent de fondements théoriques. Cette thèse vise à développer une procédure de sélection de covariables en grande dimension pour les modèles non-linéaires à effets mixtes, en étudiant leurs implémentations pratiques et leurs propriétés théoriques. Cette procédure est basée sur l'utilisation d'un prior spike-and-slab gaussien et de l'algorithme SAEM (Stochastic Approximation of Expectation Maximisation Algorithm). Des taux de contraction a posteriori autour des vraies valeurs des paramètres dans un modèle non-linéaire à effets mixtes sous prior spike-and-slab discret ont été obtenus, comparables à ceux observés dans des modèles linéaires. Les travaux conduits dans cette thèse sont motivés par des questions appliquées en amélioration des plantes, où ces modèles décrivent le développement des plantes en fonction de leurs génotypes et des conditions environnementales. Les covariables considérées sont généralement nombreuses puisque les variétés sont caractérisées par des milliers de marqueurs génétiques, dont la plupart n'ont aucun effet sur certains traits phénotypiques. La méthode statistique développée dans la thèse est appliquée à un jeu de données réel relatif à cette application<br>Mixed-effects models analyze observations collected repeatedly from several individuals, attributing variability to different sources (intra-individual, inter-individual, residual). Accounting for this variability is essential to characterize the underlying biological mechanisms without biais. These models use covariates and random effects to describe variability among individuals: covariates explain differences due to observed characteristics, while random effects represent the variability not attributable to measured covariates. In high-dimensional context, where the number of covariates exceeds the number of individuals, identifying influential covariates is challenging, as selection focuses on latent variables in the model. Many procedures have been developed for linear mixed-effects models, but contributions for non-linear models are rare and lack theoretical foundations. This thesis aims to develop a high-dimensional covariate selection procedure for non-linear mixed-effects models by studying their practical implementations and theoretical properties. This procedure is based on the use of a gaussian spike-and-slab prior and the SAEM algorithm (Stochastic Approximation of Expectation Maximisation Algorithm). Posterior contraction rates around true parameter values in a non-linear mixed-effects model under a discrete spike-and-slab prior have been obtained, comparable to those observed in linear models. The work in this thesis is motivated by practical questions in plant breeding, where these models describe plant development as a function of their genotypes and environmental conditions. The considered covariates are generally numerous since varieties are characterized by thousands of genetic markers, most of which have no effect on certain phenotypic traits. The statistical method developed in the thesis is applied to a real dataset related to this application

On s'intéresse d'abord au modèle de suite gaussienne parcimonieuse. Une approche bayésienne empirique sur l'a priori Spike and Slab permet d'obtenir la convergence à vitesse minimax du moment d'ordre 2 a posteriori pour des Slabs Cauchy et on prouve un résultat de sous-optimalité pour un Slab Laplace. Un meilleur choix de Slab permet d'obtenir la constante exacte. Dans le modèle d'estimation de densité, un a priori arbre de Polya tel que les variables de l'arbre ont une distribution de type Spike and Slab donne la convergence à vitesse minimax et adaptative pour la norme sup de la loi a posteriori et un théorème Bernstein-von Mises non paramétrique<br>The first main focus is the sparse Gaussian sequence model. An Empirical Bayes approach is used on the Spike and Slab prior to derive minimax convergence of the posterior second moment for Cauchy Slabs and a suboptimality result for the Laplace Slab is proved. Next, with a special choice of Slab convergence with the sharp minimax constant is derived. The second main focus is the density estimation model using a special Polya tree prior where the variables in the tree construction follow a Spike and Slab type distribution. Adaptive minimax convergence in the supremum norm of the posterior distribution as well as a nonparametric Bernstein-von Mises theorem are obtained

We study how to perform effective Bayesian inference in high-dimensional sparse Factor Analysis models with a zero-norm, sparsity-inducing prior on the model parameters. Such priors represent a methodological ideal, but Bayesian inference in such models is usually regarded as impractical. We test this view. After empirically characterising the properties of existing algorithmic approaches, we use techniques from statistical mechanics to derive a theory of optimal learning in the restricted setting of sparse PCA with a single factor. Finally, we describe a novel `Dense Message Passing' algorithm (DMP) which achieves near-optimal performance on synthetic data generated from this model.DMP exploits properties of high-dimensional problems to operate successfully on a densely connected graphical model. Similar algorithms have been developed in the statistical physics community and previously applied to inference problems in coding and sparse classification. We demonstrate that DMP out-performs both a newly proposed variational hybrid algorithm and two other recently published algorithms (SPCA and emPCA) on synthetic data while it explains at least the same amount of variance, for a given level of sparsity, in two gene expression datasets used in previous studies of sparse PCA.A significant potential advantage of DMP is that it provides an estimate of the marginal likelihood which can be used for hyperparameter optimisation. We show that, for the single factor case, this estimate exhibits good qualitative agreement both with theoretical predictions and with the hyperparameter posterior inferred by a collapsed Gibbs sampler. Preliminary work on an extension to inference of multiple factors indicates its potential for selecting an optimal model from amongst candidates which differ both in numbers of factors and their levels of sparsity.

We develop statistical methods for tackling two important problems in genetic association studies. First, we propose a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable model for analyzing longitudinal family data with pleiotropic phenotypes. Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated genetic variant from the initial discovery samples. It is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in the low power studies. We investigate the performance of the method with simulations and applications to four real data examples. Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques. We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.