Abstract
Despite considerable progress in, and development of, maximum entropy and Bayesian techniques, a complete understanding of the process combining noise with incomplete information remains elusive. The underdetermined problem with noisy data is here re-examined, and various results are discussed, compared, and criticized. Specific examples suggesting a resolution are presented.
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References
Bretthorst, G.L.: 1988, Bayesian Spectrum Analysis and Parameter Estimation, Springer-Verlag, Berlin.
Burg, J.P.: 1975, Maximum Entropy Spectral Analysis’, Ph.D. thesis, Stanford University (unpublished).
Gull, S.F.: 1988, Bayesian Inductive Inference and Maximum Entropy’, in G.J. Erickson and C.R. Smith (eds.), Maximum Entropy and Bayesian Methods in Science and Engineering, Vol. 1, Kluwer, Dordrecht.
Gull, S.F.: 1989, Developments in Maximum Entropy and Data Analysis’, in J. Skilling, (ed.), Maximum Entropy and Bayesian Methods, Kluwer, Dordrecht.
Gull, S.F., and G.J. Daniell: 1978, Image Reconstruction from Incomplete and Noisy Data’, Nature, 272, 686.
Jaynes, E.T.: 1963, E.T.: 1963, Information Theory and Statistical Mechanics’, in K. Ford (ed.). 1962
Brandeis Summer Institute in Theoretical Physics, Benjamin, New York.
Jaynes, E.T.: 1982, On the Rationale of Maximum-Entropy Methods’, Proc. IEEE 70, 939.
Jaynes, E.T.: 1987, Bayesian Spectrum and Chirp Analysis’, C.R. Smith and G.J. Erickson,(eds.), Maximum-Entropy and Bayesian Spectral Analysis and Estimation Problems, Reidel, Dordrecht.
Jeffreys, H.: 1939, Theory of Probability, Clarendon Press, Oxford.
Skilling, J.: 1989, Classic Maximum Entropy’, in J. Skilling, (ed.), Maximum Entropy and Bayesian Methods, Kluwer, Dordrecht.
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© 1993 Springer Science+Business Media Dordrecht
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Grandy, W.T. (1993). Noise in the Underdetermined Problem. In: Mohammad-Djafari, A., Demoment, G. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2217-9_29
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DOI: https://doi.org/10.1007/978-94-017-2217-9_29
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4272-9
Online ISBN: 978-94-017-2217-9
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