Abstract
In statistics, one has data and from this tries to infer something about its source. Estimating the probability law that gave rise to the data is one of the chief problems of this kind. Once known, its variance, confidence limits, and all other parameters describing fluctuation may be determined. Two major schools of thought on forming the estimates are the classical and the Bayesian approaches. These are compared in Chap. 16. A third approach is the use of an invariance principle (Sect. 5.14, Ex. 9.2.1 and Chap. 17). A fourth is based upon the use of Fisher information (Chap. 17). A major difference among these four approaches is their aims: the Bayesian approach is content to form a “reasonable estimate” of the unknown law, while the others seek the exact answer.
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References
E.T. Jaynes: IEEE Trans. SSC-4, 227 (1968)
N.N. Chenkov: Soviet Math. Dokl. 3, 1559 (1962); E.L. Kosarev: Comput. Phys. Commun. 20, 69 (1980)
J. MacQueen, J. Marschak: Proc. Natl. Acad. Sci. USA 72, 3819 (1975)
R. Kikuchi, B.H. Soffer: J. Opt. Soc. Am. 67, 1656 (1977)
J.P. Burg: “Maximum entropy spectral analysis,” 37th Annual Soc. Exploration Geo-physicists Meeting, Oklahoma City, 1967
S.J. Wernecke, L.R. D’Addario: IEEE Trans. C-26, 352 (1977)
B.R. Frieden: Proc. IEEE 73, 1764 (1985)
S. Goldman: Information Theory (Prentice-Hall, New York 1953)
A. Papoulis: Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York 1965)
D. Marcuse: Engineering Quantum Electrodynamics (Harcourt, Brace and World, New York 1970)
L. Mandel, E. Wolf: Rev. Mod. Phys. 37, 231 (1965)
B.R. Frieden: J. Opt. Soc. Am. 73, 927 (1983)
Additional Reading
Baierlein, R.: Atoms and Information Theory (Freeman, San Francisco 1971)
Boyd, D. W, J.M. Steele: Ann. Statist. 6, 932 (1978)
Brillouin, L.: Science and Information Theory (Academic, New York 1962)
Frieden, B. R.: Comp. Graph. Image Proc. 12, 40 (1980)
Kullbach, S.: Information Theory and Statistics (Wiley, New York 1959)
Sklansky, J., G.N. Wassel: Pattern Classifiers and Trainable Machines (Springer, Berlin, Heidelberg, New York 1981)
Tapia, R. A., J.R. Thompson: Nonparametric Probability Density Estimation (Johns Hopkins University Press, Baltimore 1978)
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© 2001 Springer-Verlag Berlin Heidelberg
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Frieden, B.R. (2001). Introduction to Estimating Probability Laws. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56699-8_10
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DOI: https://doi.org/10.1007/978-3-642-56699-8_10
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