Why Maximum Entropy? A Non-axiomatic Approach

Details Why Maximum Entropy? A Non-axiomatic Approach Why Maximum Entropy? A Non-axiomatic Approach

2002-12-02

arxiv.org/abs/math-ph/0212005v1

In: Bayesian inference and Maximum Entropy methods in Science and Engineering, R. L. Fry (ed.), AIP (Melville), 375-379, 2002

Physics

Mathematical Physics

4 pages, MaxEnt 2001

Scientific paper

Ill-posed inverse problems of the form y = X p where y is J-dimensional vector of a data, p is m-dimensional probability vector which cannot be measured directly and matrix X of observable variables is a known J,m matrix, J < m, are frequently solved by Shannon's entropy maximization (MaxEnt). Several axiomatizations were proposed to justify the MaxEnt method (also) in this context. The main aim of the presented work is two-fold: 1) to view the concept of complementarity of MaxEnt and Maximum Likelihood (ML) tasks from a geometric perspective, and consequently 2) to provide an intuitive and non-axiomatic answer to the 'Why MaxEnt?' question.

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