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Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later…

In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…

In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…

Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…

Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric…

Hydrogeologic models are commonly over-smoothed relative to reality, owing to the difficulty of obtaining accurate high-resolution information about the subsurface. When used in an inversion context, such models may introduce systematic…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a…

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while…

Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…