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Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET…
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
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 propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems. Our method applies to all Bayesian models that are log-concave, where maximum-a-posteriori (MAP) estimation is a convex optimization problem.…
Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…
Simulation-based inference (SBI) provides a powerful framework for inferring posterior distributions of stochastic simulators in a wide range of domains. In many settings, however, the posterior distribution is not the end goal itself --…
Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…
Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function such as expected improvement (EI). In practice, BO often concentrates evaluations…
We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…
We introduce a deep learning accelerated methodology to solve PDE-based Bayesian inverse problems with guaranteed accuracy. This is motivated by the ill-posed problem of inferring a spatio-temporal heat-flux parameter known as the Biot…
To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate,…
In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a…
Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from…
We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…
Current deep learning-based solutions for image analysis tasks are commonly incapable of handling problems to which multiple different plausible solutions exist. In response, posterior-based methods such as conditional Diffusion Models and…
Uncertainty in the prediction of future weather is commonly assessed through the use of forecast ensembles that employ a numerical weather prediction model in distinct variants. Statistical postprocessing can correct for biases in the…