MARIN Jean Michel

In the medical field, the use of features extracted from images is more and more widespread. These measures can be real numbers (volume, cognitive score), organ meshes or the image itself. In these last two cases, a Euclidean space cannot describe the space of measures and it is necessary to place oneself on a Riemannian variety. Using this Riemannian framework and mixed effects models, it is then possible to estimate a representative object of the population as well as the inter-individual variability. In the longitudinal case (subjects observed repeatedly over time), these models allow to create an average trajectory representative of the global evolution of the population. In this thesis, we propose to generalize these models in the case of a mixed population. Each sub-population can follow different dynamics over time and their representative trajectory can be the same or differ from one time interval to another. This new model allows for example to model the onset of a disease as a deviation from normal aging.We are also interested in the detection of anomalies (e.g. tumors) in a population. With an object representing a control population, we define an anomaly as what cannot be reconstructed by diffeomorphic deformation of this representative object. Our method has the advantage of requiring neither a large dataset nor annotation by physicians and can be easily applied to any organ.Finally, we focus on different theoretical properties of the estimation algorithms used. In the context of nonlinear mixed effects models, the MCMC-SAEM algorithm is used. We will discuss two theoretical limitations. First, we will lift the geometric ergodicity assumption by replacing it with a sub-geometric ergodicity assumption. Furthermore, we will focus on a method to apply the SAEM algorithm when the joint distribution is not exponentially curved. We will show that this method introduces a bias in the estimate that we will measure. We will also propose a new algorithm to reduce it.

The AbcRanger library provides methodologies for model choice and parameter estimation based on fast and scalable Random Forests, tuned to handle large and/or high dimensional datasets. The library, initially intended for the population genetics ABC framework DIYABC, has been generalized to any ABC reference table generator. At first, computational issues were encountered with the reference ABC-Random Forest. Those issues have been diagnosed by us as friction between "strict" Machine Learning setup and ABC context, and this incited us to modify the C++ implementation of state-of-the-art random forests, ranger, to tailor it for ABC needs: potentially "deep" decision trees are not stored in memory anymore, but are processed by batches in parallel. We focused on memory and thread scalability, ease of use (minimal hyperparameter set). R and python interfaces are provided.

Measurements are an everyday act, they give us a lot of information and allow us to make decisions. The analysis of measurements can allow us to learn more about our environment, but the error of a measurement can have important consequences in certain fields. In a first part, we propose, thanks to the study of blood analysis measurements carried out at the University Hospital of Clermont-Ferrand, a procedure allowing to detect the drifts of the analyzers of medical biology laboratories, based on the measurements of patients' analyses. After a descriptive analysis of the data, the method implemented, using methods for detecting breaks in time series, is tested for simulations of breaks representing shifts, inaccuracies or drifts of analyzers for different biological parameters measured. The method is adapted for two scenarios: when the patients' hospital service is known or not. The study is completed by an analysis of the impact of the measurement uncertainty on the patients' analyses. In a second part we study measurements of volcanic ash shapes made at the Magmas and Volcanoes Laboratory of the University of Clermont Auvergne, in order to determine a link between the collection locations and the particle shapes. After having shown the dependence between these parameters, we propose, thanks to a classification method, a grouping of the particles representing different populations depending on the distance between the collection sites and the crater of the volcano.

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This chapter surveys the most standard Monte Carlo methods available for simulating from a posterior distribution associated with a mixture and conducts some experiments about the robustness of the Gibbs sampler in high dimensional Gaussian settings. This is a chapter prepared for the forthcoming 'Handbook of Mixture Analysis'.

Gene expression is tightly controlled to ensure a wide variety of functions and cell types. The development of diseases, especially cancers, is invariably linked to the deregulation of these controls. Our goal is to model the link between gene expression and the nucleotide composition of different regulatory regions of the genome. We propose to address this problem in a regression framework with a Lasso approach coupled to a regression tree. We use exclusively sequence data and learn a different model for each cell type. We show (i) that the different regulatory regions provide different and complementary information and (ii) that the sole information of their nucleotide composition allows us to predict gene expression with an error comparable to that obtained using experimental data. Furthermore, the learned linear model does not perform as well for all genes, but better models certain classes of genes with particular nucleotide compositions.

This note is a collection of several discussions of the paper "Beyond subjective and objective in statistics", read by A. Gelman and C. Hennig to the Royal Statistical Society on April 12, 2017, and to appear in the Journal of the Royal Statistical Society, Series A.

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For in vivo research experiments with small sample sizes and available historical data, we propose a sequential Bayesian method for the Behrens-Fisher problem. We consider it as a model choice question with two models in competition: one for which the two expectations are equal and one for which they are different. The choice between the two models is performed through a Bayesian analysis, based on a robust choice of combined objective and subjective priors, set on the parameters space and on the models space. Three steps are necessary to evaluate the posterior probability of each model using two historical datasets similar to the one of interest. Starting from the Jeffreys prior, a posterior using a first historical dataset is deduced and allows to calibrate the Normal-Gamma informative priors for the second historical dataset analysis, in addition to a uniform prior on the model space. From this second step, a new posterior on the parameter space and the models space can be used as the objective informative prior for the last Bayesian analysis. Bayesian and frequentist methods have been compared on simulated and real data. In accordance with FDA recommendations, control of type I and type II error rates has been evaluated. The proposed method controls them even if the historical experiments are not completely similar to the one of interest.

This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. The stakes are high and the reader determines the outcome. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. This works in conjunction with the bayess package. Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels, as exemplified by courses given at Université Paris Dauphine (France), University of Canterbury (New Zealand), and University of British Columbia (Canada). It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics. A strength of the text is the noteworthy emphasis on the role of models in statistical analysis. This is the new, fully-revised edition to the book Bayesian Core: A Practical Approach to Computational Bayesian Statistics.