dorsal/arxiv
View SchemaBayesian inference for inverse problems
| Authors | Ali Mohammad-Djafari |
|---|---|
| Categories | |
| ArXiv ID | physics/0110093 |
| URL | https://arxiv.org/abs/physics/0110093 |
| DOI | 10.1063/1.1477067 |
Abstract
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 necessary tools we need to solve real inverse problems: starting by simple inversion where we assume to know exactly the forward model and all the input model parameters up to more realistic advanced problems of myopic or blind inversion where we may be uncertain about the forward model and we may have noisy data. Starting by an introduction to inverse problems through a few examples and explaining their ill posedness nature, I briefly presented the main classical deterministic methods such as data matching and classical regularization methods to show their limitations. I then presented the main classical probabilistic methods based on likelihood, information theory and maximum entropy and the Bayesian inference framework for such problems. I show that the Bayesian framework, not only generalizes all these methods, but also gives us natural tools, for example, for inferring the uncertainty of the computed solutions, for the estimation of the hyperparameters or for handling myopic or blind inversion problems. Finally, through a deconvolution problem example, I presented a few state of the art methods based on Bayesian inference particularly designed for some of the mass spectrometry data processing problems.
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"abstract": "Traditionally, the MaxEnt workshops start by a tutorial day. This paper\nsummarizes my talk during 2001\u0027th workshop at John Hopkins University. The main\nidea in this talk is to show how the Bayesian inference can naturally give us\nall the necessary tools we need to solve real inverse problems: starting by\nsimple inversion where we assume to know exactly the forward model and all the\ninput model parameters up to more realistic advanced problems of myopic or\nblind inversion where we may be uncertain about the forward model and we may\nhave noisy data. Starting by an introduction to inverse problems through a few\nexamples and explaining their ill posedness nature, I briefly presented the\nmain classical deterministic methods such as data matching and classical\nregularization methods to show their limitations. I then presented the main\nclassical probabilistic methods based on likelihood, information theory and\nmaximum entropy and the Bayesian inference framework for such problems. I show\nthat the Bayesian framework, not only generalizes all these methods, but also\ngives us natural tools, for example, for inferring the uncertainty of the\ncomputed solutions, for the estimation of the hyperparameters or for handling\nmyopic or blind inversion problems. Finally, through a deconvolution problem\nexample, I presented a few state of the art methods based on Bayesian inference\nparticularly designed for some of the mass spectrometry data processing\nproblems.",
"arxiv_id": "physics/0110093",
"authors": [
"Ali Mohammad-Djafari"
],
"categories": [
"physics.data-an"
],
"doi": "10.1063/1.1477067",
"title": "Bayesian inference for inverse problems",
"url": "https://arxiv.org/abs/physics/0110093"
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