Related papers: Efficient hyperparameter estimation in Bayesian in…
We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
This work studies the inverse problem of photoacoustic tomography (more precisely, the acoustic subproblem) as the identification of a space-dependent source parameter. The model consists of a wave equation involving a time-fractional…
We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form.…
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…
Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…
We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…
This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al. (2013). This result holds in any separable…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
The recovery of sparse generative models from few noisy measurements is an important and challenging problem. Many deterministic algorithms rely on some form of $\ell_1$-$\ell_2$ minimization to combine the computational convenience of the…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
The main object of this paper is to present some general concepts of Bayesian inference and more specifically the estimation of the hyperparameters in inverse problems. We consider a general linear situation where we are given some data…
We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the small noise limit. Existing results suffer from a certain…
Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…