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This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…
This paper is concerned with a Bayesian approach to testing hypotheses in statistical inverse problems. Based on the posterior distribution $\Pi \left(\cdot |Y = y\right)$, we want to infer whether a feature $\langle\varphi,…
In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional…
We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…
We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…
We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the…
We develop a method to perform an untargeted Bayesian search for anisotropic gravitational-wave backgrounds that can efficiently and accurately reconstruct the background intensity map. Our method employs an analytic marginalization of the…
We continue the investigation of Bernstein-von Mises theorems for nonparametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined,…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…
Maximum-a-posteriori (MAP) approaches are an effective framework for inverse problems with known forward operators, particularly when combined with expressive priors and careful parameter selection. In blind settings, however, their use…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…