相关论文: Bayesian Approach to Inverse Problems: an Applicat…

This work is concerned with nonparametric goodness-of-fit testing in the context of nonlinear inverse problems with random observations. Bayesian posterior distributions based upon a Gaussian process prior distribution are proven to…

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…

We consider the problem of assessing goodness of fit of a single Bayesian model to the observed data in the inverse problem context. A novel procedure of goodness of fit test is proposed, based on construction of reference distributions…

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.…

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…

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…

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 consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…

In the bayesian analysis of Inverse Problems most relevant cases the forward maps (FM, or regressor function) are defined in terms of a system of (O, P)DE's with intractable solutions. These necessarily involve a numerical method to find…

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…

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…

We consider the generic problem of performing a global fit to many independent data sets each with a different overall multiplicative normalization uncertainty. We show that the methods in common use to treat multiplicative uncertainties…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

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…

The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…

For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…