Related papers: Non-asymptotic error estimates for the Laplace app…

Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…

Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…

In Bayesian inference, a widespread technique to compute integrals against a high-dimensional posterior is to use a Gaussian proxy to the posterior known as the Laplace approximation. We address the question of accuracy of the approximation…

Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the…

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…

Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters, which are parameters that contribute to the overall…

In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…

We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…

For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear inverse problem of recovering the conductivity $f>0$ in the divergence form equation $$…

We consider the inverse problem of recovering an unknown functional parameter $u$ in a separable Banach space, from a noisy observation $y$ of its image through a known possibly non-linear ill-posed map ${\mathcal G}$. The data $y$ is…

This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior…

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…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…