Related papers: Bayesian inverse problems with unknown operators
Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the…
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
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…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
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,…
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…
We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement…
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
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…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
In this article, the solution of a statistical inverse problem $M = AU+\mathcal{E}$ by the Bayesian approach is studied where $U$ is a function on the unit circle $\mathbb{T}$, i.e., a periodic signal. The mapping $A$ is a smoothing linear…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…