A maximum entropy method when prior information consists of inexact constraints

Details A maximum entropy method when prior information consists of inexact constraints A maximum entropy method when prior information consists of inexact constraints

Feb 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...422..845l&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 422, no. 2, p. 845-849

Physics

Condensed Matter

Statistical Mechanics

1

Astronomical Models, Computerized Simulation, Constraints, Mathematical Models, Maximum Entropy Method, Statistical Analysis, Image Reconstruction, Information Theory, Spectra, Spectrum Analysis, Statistical Mechanics

Scientific paper

Curve fitting to experimental spectra or image reconstruction in astrophysics and other experimental disciplines can be charaterized in the context of maximum entropy methods as seeking a distribution of high entropy consistent with the data. Many authors have adopted an ad hoc approach of maximizing the statistic S - lambda(chi2), where S is the Shannon entropy of the fitted distribution and chi2 is the usual statistical measure of agreement between certain properties of the fitted distribution and those of the data. This paper points out that this approach arises naturally in terms of a simple conceptual model, similar to models advanced in support of maximum entropy methods in the case of precise constraints on the fitted distribution. Numerical simulations illustrate the procedure. It is suggested that a preferred choice for the free parameter lambda is (2r)-1, where r is the number of pixels in the image (or channels in the spectrum).

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