
Inverse heat source problem and experimental design for determining iron loss distribution
Iron loss determination in the magnetic core of an electrical machine, s...
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A Bayesian level set method for an inverse medium scattering problem in acoustics
In this work, we are interested in the determination of the shape of the...
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Continuum Limit of Posteriors in Graph Bayesian Inverse Problems
We consider the problem of recovering a function input of a differential...
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Allatonce formulation meets the Bayesian approach: A study of two prototypical linear inverse problems
In this work, the Bayesian approach to inverse problems is formulated in...
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On the wellposedness of Bayesian inverse problems
The subject of this article is the introduction of a weaker concept of w...
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Posterior contraction rates for nonparametric state and drift estimation
We consider a combined state and drift estimation problem for the linear...
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A statistical framework for modelbased inverse problems in ultrasound elastography
Modelbased computational elasticity imaging of tissues can be posed as ...
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Stabilities of Shape Identification Inverse Problems in a Bayesian Framework
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 finitedimensional observation data with some Gaussian random noise. Then, the stability of posterior is studied for observation data. For each point of the space, the conditional probability that the point is included in the unknown domain given the observation data is considered. The stability is also studied for this probability distribution. As a model problem for our inverse problem, a heat inverse problem is considered. This problem requires the determination of the unknown shape of cavities in a heat conductor from temperature data of some portion of the surface of the heat conductor. To apply the above stability results to this model problem, one needs the measurability and some boundedness of the forward operator. These properties are shown.
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