Mathematics – Statistics Theory
Scientific paper
2000-09-13
In: Bayesian inference and Maximum Entropy methods in Science and Engineering, A. Mohammad-Djafari (ed.), AIP (Melville), pp.
Mathematics
Statistics Theory
Presented at 'MaxEnt 2000', CNRS, Gif sur Yvette, France, July 8-13 2000
Scientific paper
10.1063/1.1381870
Concept of exponential family is generalized by simple and general exponential form. Simple and general potential are introduced. Maximum Entropy and Maximum Likelihood tasks are defined. ML task on the simple exponential form and ME task on the simple potentials are proved to be complementary in set-up and identical in solutions. ML task on the general exponential form and ME task on the general potentials are weakly complementary, leading to the same necessary conditions. A hypothesis about complementarity of ML and MiniMax Entropy tasks and identity of their solutions, brought up by a special case analytical as well as several numerical investigations, is suggested in this case. MiniMax Ent can be viewed as a generalization of MaxEnt for parametric linear inverse problems, and its complementarity with ML as yet another argument in favor of Shannon's entropy criterion.
Grendar Marian
jr
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