Related papers: Learning to solve Bayesian inverse problems: An am…
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…
Bayesian observer and actor models have provided normative explanations for many behavioral phenomena in perception, sensorimotor control, and other areas of cognitive science and neuroscience. They attribute behavioral variability and…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…
By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…
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…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
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…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
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…
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…
Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
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.…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…