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Harper and C.A. Hooker, eds. (Dordrecht: Reidel). [1]Jaynes, E.T. 1985, in Maximum-Entropy and Bayesian Methods in Inverse Problems, C.R. Smithand W.T. Grandy, Jr., eds. (Dordrecht: Reidel). [2]Jaynes, E.T. 1984, in SIAM-AMS Proceedings, vol. 14, D.W. McLaughlin, ed. (Providence, RI:American Mathematical Society). [3]Titterington, D.M. 1985, Astronomy and Astrophysics, vol. 144, 381–387. [4]Narayan, R., and Nityananda, R.
1986, Annual Review of Astronomy and Astrophysics, vol. 24,pp. 127–170. [5]Skilling, J., and Bryan, R.K. 1984, Monthly Notices of the Royal Astronomical Society, vol. 211,pp. 111–124. [6]Burch, S.F., Gull, S.F., and Skilling, J. 1983, Computer Vision, Graphics and Image Processing,vol. 23, pp. 113–128.
[7]Skilling, J. 1989, in Maximum Entropy and Bayesian Methods, J. Skilling, ed. (Boston: Kluwer). [8]Frieden, B.R. 1983, Journal of the Optical Society of America, vol. 73, pp. 927–938. [9]Skilling, J., and Gull, S.F. 1985, in Maximum-Entropy and Bayesian Methods in Inverse Problems,C.R. Smith and W.T.
Grandy, Jr., eds. (Dordrecht: Reidel). [10]Skilling, J. 1986, in Maximum Entropy and Bayesian Methods in Applied Statistics, J.H. Justice,ed. (Cambridge: Cambridge University Press). [11]Cornwell, T.J., and Evans, K.F. 1985, Astronomy and Astrophysics, vol. 143, pp. 77–83.
[12]Gull, S.F. 1989, in Maximum Entropy and Bayesian Methods, J. Skilling, ed. (Boston: Kluwer).[13]Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited.
To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).• Better priors: We already noted that the entropy functional (equation18.7.13) is invariant under scrambling all pixels and has no notion ofsmoothness. The so-called “intrinsic correlation function” (ICF) model(Ref. [13] , where it is called “New MaxEnt”) is similar enough to theentropy functional to allow similar algorithms, but it makes the values ofneighboring pixels correlated, enforcing smoothness.• Better estimation of λ: Above we chose λ to bring χ2 into its expectednarrow statistical range of N ± (2N )1/2 .
This in effect overestimates χ2 ,however, since some effective number γ of parameters are being “fitted”in doing the reconstruction. A Bayesian approach leads to a self-consistentestimate of this γ and an objectively better choice for λ..
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