Related papers: The Brouwer Lecture 2005: Statistical estimation w…

We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To…

We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…

In this article, we introduce a new variable selection technique through trimming for finite mixture of regression models. Compared to the traditional variable selection techniques, the new method is robust and not sensitive to outliers.…

We consider the problem of estimating an expected outcome from a stochastic simulation model. Our goal is to develop a theoretical framework on importance sampling for such estimation. By investigating the variance of an importance sampling…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…

We provide a brief overview of both Bayes and classical model selection. We argue tentatively that model selection has at least two major goals, that of finding the correct model or predicting well, and that in general both these goals may…

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…

Statistical modeling is a powerful tool for developing and testing theories by way of causal explanation, prediction, and description. In many disciplines there is near-exclusive use of statistical modeling for causal explanation and the…

For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…

The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

The purpose of this paper is to pursue our study of rho-estimators built from i.i.d. observations that we defined in Baraud et al. (2014). For a \rho-estimator based on some model S (which means that the estimator belongs to S) and a true…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and…

A standard goal of model evaluation and selection is to find a model that approximates the truth well while at the same time is as parsimonious as possible. In this paper we emphasize the point of view that the models under consideration…

Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as…

This work is motivated by learning the individualized minimal clinically important difference, a vital concept to assess clinical importance in various biomedical studies. We formulate the scientific question into a high-dimensional…

The fact that we can build models from data, and therefore refine our models with more data from experiments, is usually given for granted in scientific inquiry. However, how much information can we extract, and how precise can we expect…