Estelle Kuhn

Recovering Power in Association Mapping Panels with Variable Levels of Linkage Disequilibrium

Association mapping has permitted the discovery of major QTL in many species. It can be applied to existing populations and, as a consequence, it is generally necessary to take into account structure and relatedness among individuals in the statistical model to control false positives. We analytically studied power in association studies by computing noncentrality parameter of the tests and its relationship with parameters characterizing diversity (genetic differentiation between groups and allele frequencies) and kinship between individuals. Investigation of three different maize diversity panels genotyped with the 50k SNPs array highlighted contrasted average power among panels and revealed gaps of power of classical mixed models in regions with high linkage disequilibrium (LD). These gaps could be related to the fact that markers are used for both testing association and estimating relatedness. We thus considered two alternative approaches to estimating the kinship matrix to recover power in regions of high LD. In the first one, we estimated the kinship with all the markers that are not located on the same chromosome than the tested SNP. In the second one, correlation between markers was taken into account to weight the contribution of each marker to the kinship. Simulations revealed that these two approaches were efficient to control false positives and were more powerful than classical models.

Convergence of the Wang-Landau algorithm

We analyze the convergence properties of the Wang-Landau algorithm. This sampling method belongs to the general class of adaptive importance sampling strategies which use the free energy along a chosen reaction coordinate as a bias. Such algorithms are very helpful to enhance the sampling properties of Markov Chain Monte Carlo algorithms, when the dynamics is metastable. We prove the convergence of the Wang-Landau algorithm and an associated central limit theorem.

Convergent stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation

Estimation in the deformable template model is a big challenge in image analysis. The issue is to estimate an atlas of a population. This atlas contains a template and the corresponding geometrical variability of the observed shapes. The goal is to propose an accurate estimation algorithm with low computational cost and with theoretical guaranties of relevance. This becomes very demanding when dealing with high dimensional data, which is particularly the case of medical images. The use of an optimized Monte Carlo Markov Chain method for a stochastic Expectation Maximization algorithm, is proposed to estimate the model parameters by maximizing the likelihood. A new Anisotropic Metropolis Adjusted Langevin Algorithm is used as transition in the MCMC method. First it is proven that this new sampler leads to a geometrically uniformly ergodic Markov chain. Furthermore, it is proven also that under mild conditions, the estimated parameters converge almost surely and are asymptotically Gaussian distributed. The methodology developed is then tested on handwritten digits and some 2D and 3D medical images for the deformable model estimation. More widely, the proposed algorithm can be used for a large range of models in many fields of applications such as pharmacology or genetic. The technical proofs are detailed in an appendix.11The appendix is available as supplementary material (see Appendix A).

Bayesian Mixed Effect Atlas Estimation with a Diffeomorphic Deformation Model

In this paper we introduce a diffeomorphic constraint on the deformations considered in the deformable Bayesian mixed effect template model. Our approach is built on a generic group of diffeomorphisms, which is parameterized by an arbitrary set of control point positions and momentum vectors. This enables us to estimate the optimal positions of control points together with a template image and parameters of the deformation distribution which compose the atlas. We propose to use a stochastic version of the expectation-maximization algorithm where the simulation is performed using the anisotropic Metropolis adjusted Langevin algorithm. We propose also an extension of the model including a sparsity constraint to select an optimal number of control points with relevant positions. Experiments are carried out on the United States Postal Service database, on mandibles of mice, and on three-dimensional murine dendrite spine images.

On a convergent stochastic estimation algorithm for frailty models

A maximum likelihood estimation procedure is presented for the frailty model. The procedure is based on a stochastic Expectation Maximization algorithm which converges quickly to the maximum likelihood estimate. The usual expectation step is replaced by a stochastic approximation of the complete log-likelihood using simulated values of unobserved frailties whereas the maximization step follows the same lines as those of the Expectation Maximization algorithm. The procedure allows to obtain at the same time estimations of the marginal likelihood and of the observed Fisher information matrix. Moreover, this stochastic Expectation Maximization algorithm requires less computation time. A wide variety of multivariate frailty models without any assumption on the covariance structure can be studied. To illustrate this procedure, a Gaussian frailty model with two frailty terms is introduced. The numerical results based on simulated data and on real bladder cancer data are more accurate than those obtained by using the Expectation Maximization Laplace algorithm and the Monte-Carlo Expectation Maximization one. Finally, since frailty models are used in many fields such as ecology, biology, economy, …, the proposed algorithm has a wide spectrum of applications.