Bayesian inverse problems for functions and applications to fluid mechanics

By Simon L. Cotter, Masoumeh Dashti, James C. Robinson, Andrew M. Stuart. 2009

197 citations recorded by the source corpus.

Subfields: Geophysics, Mechanical Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/0d89e3865d5789f2a129d92b5a7dc5d29acea4ca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geophysics

1. Andrew M. Stuart
2. Sari Lasanen
3. Kody J. H. Law
4. Heng Xiao

In Mechanical Engineering

1. Andrew M. Stuart
2. Sari Lasanen
3. Kody J. H. Law
4. Konstantinos C. Zygalakis

In Ocean Engineering

1. Andrew M. Stuart
2. Sari Lasanen
3. Kody J. H. Law
4. Konstantinos C. Zygalakis
5. Masoumeh Dashti
6. Simon L. Cotter
7. Heng Xiao

Citations in the corpus

• Non-Gaussian statistical inverse problems. Part I: Posterior distributions (2012, methodology): “The starting point in [22, 23, 120] is that the posterior distribution is assumed to have Radon-Nikodym density with respect to the prior distribution.”
• Data Assimilation: A Mathematical Introduction (2015, methodology): “This idea is used for data assimilation problems arising in fluid mechanics in [28], for inverse problems arising in subsurface geophysics in [36, 34] and described more generally in [106].”
• Besov priors for Bayesian inverse problems (2011, background): “Our aim here is to generalize the results of [7, 30] to the case of Besov prior measures and so we need a similar Fernique-like result for the Besov measures.”
• The Bayesian Approach to Inverse Problems (2013, background): “General development of Bayes’ Theorem for inverse problems on function space, along the lines described here, may be found in [17, 92].”
• MAP estimators and their consistency in Bayesian nonparametric inverse problems (2013, background): “then under the preceding assumptions the Bayesian inverse problem for the posterior measure μ for u|y is well-defined and is Lipschitz in y with respect to the Hellinger metric (see [7]).”
• MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, methodology): “Both the data assimilation inverse problems from subsection 2.2 are shown to satisfy Assumptions 6.1, for appropriate choice of X in [15] (Navier-Stokes) and [61] (Stokes).”
• Inverse problems: A Bayesian perspective (2010, methodology): “Lemma 3.12 and Theorem 3.13, arising in the study of Lagrangian observations, are proved in Cotter et al. (2009) (Navier–Stokes case) and Cotter et al. (2010a) (Stokes case).”