International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 16.2, pp. 346-347
Section 16.2.2.3. Jaynes' maximum-entropy principle
aLaboratory of Molecular Biology, Medical Research Council, Cambridge CB2 2QH, England |
From the fundamental theorems just stated, which may be recognized as Gibbs' argument in a different guise, Jaynes' own maximum-entropy argument proceeds with striking lucidity and constructive simplicity, along the following lines:
The only requirement for this analysis to be applicable is that the `ranges of possibilities' to which it refers should be representable (or well approximated) by ensembles of abstract messages emanating from a random source. The entropy to be maximized is then the entropy per symbol of that source.
The final form of the maximum-entropy criterion is thus that q(s) should be chosen so as to maximize, under the constraints expressing the knowledge of newly acquired data, its entropy relative to the `prior prejudice' m(s) which maximizes H in the absence of these data.