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In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Fast development in science and technology has driven the need for proper statistical tools to capture special data features such as abrupt changes or sharp contrast. Many inverse problems in data science require spatiotemporal solutions…
While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter…
In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…
Precise temperature measurements on systems of few ultracold atoms is of paramount importance in quantum technologies, but can be very resource-intensive. Here, we put forward an adaptive Bayesian framework that substantially boosts the…
Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard…
Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems.…
Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies within the class of multifidelity problems, where a variety…
This work proposes an adaptive sequential Monte Carlo sampling algorithm to solve Bayesian inverse problems in scenarios where likelihood evaluations are costly but can be approximated using a surrogate model built from previous evaluations…
In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…
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.…
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…
We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…
Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…
Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…