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The maximum‐entropy method without the positivity constraint – applications to the determination of the distance‐distribution function in small‐angle scattering
Author(s) -
Steenstrup S.,
Hansen S.
Publication year - 1994
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889894000932
Subject(s) - underdetermined system , principle of maximum entropy , entropy (arrow of time) , constraint (computer aided design) , maximum entropy method , mathematics , statistical physics , function (biology) , scattering , distribution function , distribution (mathematics) , algorithm , physics , mathematical analysis , statistics , optics , geometry , thermodynamics , evolutionary biology , biology
The maximum‐entropy principle (MaxEnt) is well suited to the solution of underdetermined problems by inclusion of prior knowledge in a logically consistent way. In most applications of MaxEnt, a set of numbers – pixel densities in an image or counts in a spectrum – are determined. In these cases, the set of numbers can be interpreted as a probability distribution and is, as such, all positive. It is the purpose here to show that MaxEnt is able to provide estimates of a set of quantities that cannot necessarily be interpreted as probabilities and that may become negative, as is the case for the correlation function in small‐angle scattering. The method is illustrated both by analysis of simulated data and by measurements on sodium dodecylsulfate.