Abstract
The problem of the determination of the charge density from limited information about the charge form factor is an ill-posed inverse problem. A Bayesian probabilistic approach to this problem which permits to take into account both errors and prior information about the solution is presented. We will show that many classical methods can be considered as special cases of the proposed approach. We address also the problem of the basis function choice for the discretization and the uncertainty of the solution. Some numerical results for an analytical model are presented to show the performance of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. L. Friar and J. W. Negele, Nucl. Phys. A 212, 93 (1973).
B. Dreher et al., Nucl. Phys. A 235, 219 (1974).
J. Heisenberg and H. P. Blok, Ann. Rev. Nucl. Part. Sc. 33, 569 (1983).
D. S. Watkins, Fundamentals of Matrix Computations (Wiley, New York, 1991).
M. E. Grypeos, G. A. Lalazissis, S. E. Massen, and C. P. Panos, J. Phys. G 17, 1093 (1991).
R. E. Kozak, Am. J. Phys. 59, 74 (1991).
R. Anni, G. Co’, and P. Pellegrino, preprint (1994).
C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications (Wiley, New York, 1971).
J. Baker-Jarvis, J. Math. Phys. 30, 302 (1989).
J. Baker-Jarvis, M. Racine, and J. Alameddine, J. Math. Phys. 30, 1459 (1989).
N. Canosa, H. G. Miller, A. Piastino and R. Rossignoli, Physica A220, 611 (1995).
S. F. Gull and G.J. Daniell, Nature 272, 686 (1978).
H.G. Miller, Y. Tzeng, G.D. Yen, N. Canosa, R. Rossignoli and A. Piastino, to be published.
Buck and Macaulay, “Linear inversion by the method of maximum entropy,” in Maximum Entropy and Bayesian Methods 89, (J. Skilling, ed.), Kluwer Academic Publishers, 1990.
J. Skilling, “Classical maximum entropy” in Maximum Entropy and Bayesian Methods 89, (J. Skilling, ed.), pp. 45–52, Kluwer Academic Publishers, 1989.
A. Mohammad-Djafari, “A full Bayesian approach for inverse problems,” in Maximum Entropy and Bayesian Methods 95, (K. Hanson and R. Silver, ed.), Kluwer Academic Publishers, 1996.
D.J.C. MacKay, “Hyperparameters: Optimize or integrate out?” in Maximum Entropy and Bayesian Methods 93, (G. Heidbreder, ed.), pp. 43–59, Kluwer Academic Publishers, 1996.
V.A. Macaulay and B. Buck, “A fresh look at model selection in inverse scattering,” in Maximum Entropy and Bayesian Methods 94, (J. Skilling and S. Sibisi ed.), Kluwer Academic Publishers, 1996.
A. Mohammad-Djafari and J. Idier, “A scale invariant Bayesian method to solve linear inverse problems”, pp. 121–134. in Maximum Entropy and Bayesian Methods 94, (G. Heidbreder, ed.), Kluwer Academic Publishers, 1996.
A. Mohammad-Djafari and J. Idier, “Maximum entropy prior laws of images and estimation of their parameters,” pp. 285–293. in Maximum Entropy and Bayesian Methods 90, (T. Grandy, ed.), Kluwer Academic Publishers, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Mohammad-Djafari, A., Miller, H.G. (1998). A Bayesian Approach for the Determination of the Charge Density from Elastic Electron Scattering Data. In: Erickson, G.J., Rychert, J.T., Smith, C.R. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 98. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5028-6_13
Download citation
DOI: https://doi.org/10.1007/978-94-011-5028-6_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6111-7
Online ISBN: 978-94-011-5028-6
eBook Packages: Springer Book Archive