Maximum-entropy data analysis

The reconstruction of physical quantities from (computer-) experimental data is very often hampered by the presence of noise, insufficient information and above all by the ill-posed nature of the underlying inversion problem. It will be demonstrated that the maximum entropy concepts is particularly suited for this type of data-analysis problems. It is based on Bayesian statistics and provides a consistent probabilistic theory to obtain unbiased results, independent of any model assumptions. This is particularly desirable if there is no additional information to justify these hypotheses. If, on the other hand, additional prior knowledge is available, it can be effectively incorporated into the computation, leading to more stringent confidence intervals.

[1]  B. Frieden.  Restoring with maximum likelihood and maximum entropy. , 1972, Journal of the Optical Society of America.

[2]  Hanke,et al.  Spectral properties of the one-dimensional Hubbard model. , 1994, Physical review letters.

[3]  Andrew Keith Holland,et al.  Tomographic Analysis of the Evolution of Plasma Cross-Sections in Hbt. , 1986 .

[4]  Donath,et al.  Unbiased access to exchange splitting of magnetic bands using the maximum entropy method. , 1993, Physical review letters.

[5]  White,et al.  One-electron spectral weight of the doped two-dimensional Hubbard model. , 1994, Physical review letters.

[6]  Amir Dembo,et al.  Information theoretic inequalities , 1991, IEEE Trans. Inf. Theory.

[7]  E. Taglauer.  Investigation of the local atomic arrangement on surfaces using low-energy ion scattering , 1985 .

[8]  Schönhammer,et al.  Spectral functions for the Tomonaga-Luttinger model. , 1992, Physical review. B, Condensed matter.

[9]  Voit.  Charge-spin separation and the spectral properties of Luttinger liquids. , 1993, Physical review. B, Condensed matter.

[10]  P. Weiss,et al.  Aimantation et phénomène magnétocalorique du nickel , 1925 .

[11]  F. Haldane,et al.  Luttinger liquid theory of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas , 1981 .

[12]  Elliott H. Lieb,et al.  Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension , 1968 .

[13]  Silver,et al.  Maximum-entropy method for analytic continuation of quantum Monte Carlo data. , 1990, Physical review. B, Condensed matter.

[14]  W. T. Grandy.  Maximum entropy in action: Buck, Brian and Macaulay, Vincent A., 1991, 220 pp., Clarendon Press, Oxford, £30 pb, ISBN 0-19-8539630 , 1995 .

[15]  Anderson Pw.  Luttinger-liquid" behavior of the normal metallic state of the 2D Hubbard model. , 1990 .

[16]  John Skilling,et al.  Maximum Entropy and Bayesian Methods , 1989 .

[17]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[18]  V. Dose,et al.  Temperature behaviour of a «magnetic» band in nickel , 1989 .

[19]  T. Fauster.  Surface geometry determination by large-angle ion scattering , 1988 .