Related papers: Geometric statistical inference
We show that the Collins-Soper-Sterman resummation approach to the derivation of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is gauge invariant. The special gauge-dependent parton distribution function employed in the…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
We solve the inverse problem of deblurring a pixelized image of Jupiter using regularized deconvolution and by sample-based Bayesian inference. By efficiently sampling the marginal posterior distribution for hyperparameters, then the full…
Many inverse problems arising in applications come from continuum models where the unknown parameter is a field. In practice the unknown field is discretized resulting in a problem in $\mathbb{R}^N$, with an understanding that refining the…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the…
We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…
This work is concerned with nonparametric goodness-of-fit testing in the context of nonlinear inverse problems with random observations. Bayesian posterior distributions based upon a Gaussian process prior distribution are proven to…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…
We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…
We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
The goal of a scientific investigation is to find answers to specific questions. In geosciences this is typically achieved by solving an inference or inverse problem and interpreting the solution. However, the answer obtained is often…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…