Abstract
This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of the achievements and possible future applications of this subject to physics.
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References
1. S.-i. Amari, Differential-Geometrical Methods in Statistics, vol. 28 of Lecture Notes in Statistics, Springer-Veriag, 1985.
C. Rodriguez, “The metrics induced by the kullback number,” In Maximum Entropy and Bayesian Methods Garching, Germany 1998, J. Skilling, ed., Kluwer Academic Publishers, 1989.
D. S. R.F. Baierlein and J. Wheeler, “Three-dimensional geometry as carrier of information about time,” Phys. Rev., pp. 1864–1865, 1962.
T. Jacobson, “Thermodynamics of spacetime: The einstein equation of state,” tech. rep., xxx.lanl.gov/abs/gr-qc/9504004, 1995.
D. Hestenes, Space-Time Algebra, Gordon and Breach, N.Y., 1966.
I. Ibragimov and R. Has’minskii, Statistical Estimation, vol. 16 of Applications of Mathematics, Springer-Verlag, 1981.
D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculas. D. Reidel, 1984. For links to online resources on Clifford algebra check,.
E. Jaynes, “Information theory and statistical mechanics,” Phys. Rev., 106, p. 620, 1957. Part II; ibid, vol 108, 171.
C. Rodriguez, “Entropic priors,” tech. rep., omega.albany.edu:8008/entpriors.ps, Oct. 1991.
A. Zellner, “Past and reacent results on maximal data information priors,” tech. rep., H.G.B. Alexander Reseach Foundation. Graduate Shool of Business, University of Chicago, 1995.
B. Dubrovin, A. Fomenko, and S. Novikov, Modern Geometry-Methods and Applications, Part-I, vol. GTM 93 of Graduate Texts in Mathematics, Springer-Verlag, 1984.
C Rodríguez, “Objective bayesianism and geometry,” in Maximum Entropy and Bayesian Methods Garching, Germany 1998, P. F. Fougère, ed., Kluwer Academic Publishers, 1990.
C. Rodríguez, “Bayesian robustness: A new look from geometry,” in Maximum Entropy and Bayesian Methods Garching, Germany 1998, G. Heidbreder, ed., pp. 87–96, Kluwer Academic Publishers, 1996. (since Nov. 1993) in omega.albany.edu:8008/robust.ps.
D. Bleecker, Gauge Theory and Variational Principles, Addison-Wesley, 1981.
C. Rodríguez, “From euclid to entropy,” in Maximum Entropy and Bayesian Methods Garching, Germany 1998, W. T. Grandy, Jr., ed., Kluwer Academic Publishers. omega.albany.edu:8008/euclid.ps, 1991. omega.albany.edu:8008/euclid.ps.
J. Bekenstein Phys. Rev. D, 7, p. 2333, 1973.
S. Hawking Comm. Math. Phys., 43, p. 199, 1975.
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Rodriguez, C.C. (1999). Are We Cruising a Hypothesis Space?. In: von der Linden, W., Dose, V., Fischer, R., Preuss, R. (eds) Maximum Entropy and Bayesian Methods Garching, Germany 1998. Fundamental Theories of Physics, vol 105. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4710-1_14
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DOI: https://doi.org/10.1007/978-94-011-4710-1_14
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