Related papers: Bayesian Time-Lapse Full Waveform Inversion using …

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…

Full-waveform inversion (FWI) is known as a seismic data processing method that achieves high-resolution imaging. In the inversion part of the method that brings high resolution in finding a convergence point in the model space, a local…

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency…

Hyperspectral unmixing is a blind source separation problem which consists in estimating the reference spectral signatures contained in a hyperspectral image, as well as their relative contribution to each pixel according to a given mixture…

Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk behavior typical of many Markov Chain Monte Carlo samplers.…

Hamiltonian Flow Monte Carlo(HFMC) methods have been implemented in engineering, biology and chemistry. HFMC makes large gradient based steps to rapidly explore the state space. The application of the Hamiltonian dynamics allows to estimate…

We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…

Full Waveform Inversion (FWI) is a promising technique for achieving high-resolution imaging in medical ultrasound. However, conventional FWI methods suffer from issues related to computational efficiency, dependence on initial models, and…

This paper proposes an effective treatment of hyperparameters in the Bayesian inference of a scalar field from indirect observations. Obtaining the joint posterior distribution of the field and its hyperparameters is challenging. The…

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…

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty, which most functional alignment methods cannot…

The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the…

We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…

In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty…

Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…

This paper considers Bayesian parameter estimation of dynamic systems using a Markov Chain Monte Carlo (MCMC) approach. The Metroplis-Hastings (MH) algorithm is employed, and the main contribution of the paper is to examine and illustrate…

Bayesian inference with deep generative prior has received considerable interest for solving imaging inverse problems in many scientific and engineering fields. The selection of the prior distribution is learned from, and therefore an…