Related papers: A Robbins-Monro procedure for the estimation of pa…
For quantitative seismic imaging, iterative least-squares reverse time migration is the recommended approach. The existence of an inverse of the forward modelling operator would considerably reduce the number of required iterations. In the…
We obtain rates of convergence to stationarity in L^1-Wasserstein distance for a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in the dimension and the system parameters. The results are then…
We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a…
We consider a nonlocal approximation of the quadratic porous medium equation where the pressure is given by a convolution with a mollification kernel. It is known that when the kernel concentrates around the origin, the nonlocal equation…
The Robbins estimator is the most iconic and widely used procedure in the empirical Bayes literature for the Poisson model. On one hand, this method has been recently shown to be minimax optimal in terms of the regret (excess risk over the…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
Estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with (very) large samples of high dimensional data. The collected data may be contaminated by noise so that robust…
Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…
We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations.…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
We propose a study of a distribution registration model for general deformation functions. In this framework, we provide estimators of the deformations as well as a goodness of fit test of the model. For this, we consider a criterion which…
We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically…
In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being…
We set up Restricted Boltzmann Machines (RBM) to reproduce the Long Range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of…
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…
Adsorption is a relevant process in many fields, such as product manufacturing or pollution remediation in porous materials. Adsorption takes place at the molecular scale, amenable to be modeled by Lagrangian numerical methods. We have…
We establish exact rates of convergence in the $p$-Wasserstein distance for the empirical measure of a class of non-symmetric jump processes, which are subordinated to a diffusion process on a compact Riemannian manifold. For the quadratic…