scholarly journals All-At-Once Formulation Meets the Bayesian Approach: A Study of Two Prototypical Linear Inverse Problems

2021 ◽  
pp. 1-44
Author(s):  
Anna Schlintl ◽  
Barbara Kaltenbacher
Keyword(s):  
Inverse Problems ◽  
Bayesian Approach ◽  
Linear Inverse Problems ◽  
The Bayesian Approach

Convergence rate for the Bayesian approach to linear inverse problems

2007 ◽  
Vol 23 (6) ◽  
pp. 2469-2484 ◽  
Author(s):  
Andreas Hofinger ◽  
Hanna K Pikkarainen
Keyword(s):  
Inverse Problems ◽  
Convergence Rate ◽  
Bayesian Approach ◽  
Linear Inverse Problems ◽  
The Bayesian Approach

scholarly journals The Bayesian Approach to Inverse Problems

2017 ◽  
pp. 311-428 ◽  
Author(s):  
Masoumeh Dashti ◽  
Andrew M. Stuart
Keyword(s):  
Inverse Problems ◽  
Bayesian Approach ◽  
The Bayesian Approach

scholarly journals Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems

2013 ◽  
Vol 123 (10) ◽  
pp. 3828-3860 ◽  
Author(s):  
Sergios Agapiou ◽  
Stig Larsson ◽  
Andrew M. Stuart
Keyword(s):  
Inverse Problems ◽  
Bayesian Approach ◽  
Ill Posed ◽  
The Bayesian Approach

scholarly journals Inverse problems: A Bayesian perspective

Acta Numerica ◽  
2010 ◽  
Vol 19 ◽  
pp. 451-559 ◽  
Author(s):  
A. M. Stuart
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Bayesian Approach ◽  
Practical Importance ◽  
Full Characterization ◽  
Ill Posed ◽  
The Subject ◽  
Computational Resources ◽  
The Bayesian Approach

The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.

REFINEMENT OF RELIABILITY INDICATORS BASED ON THE BAYESIAN APPROACH IN DESIGNING 10 KV AIR LINES

2020 ◽  
pp. 55-61
Author(s):  
TAMARA B. LESHINSKAY ◽  
◽  
SERGEY I. BELOV ◽  
PAVEL S. PETROV ◽  
◽  
...  
Keyword(s):  
Bayesian Approach ◽  
Reliability Indicators ◽  
The Bayesian Approach

scholarly journals The Bayesian Approach and the Results of the ISAR-REACT 5 Trial

2021 ◽  
Vol 14 (2) ◽  
pp. 231-232
Author(s):  
Adnan Kastrati ◽  
Alexander Hapfelmeier
Keyword(s):  
Bayesian Approach ◽  
The Bayesian Approach
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