A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.
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Acknowledgements We thank O. Bozo, B. Gomberg, R.S. Melzer, A. Moscovitch-Eiger, R. Schweiger, A. Solomon and D. Zernik for discussions related to the work presented here. R.T. was partially supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.
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- Feynman calculus
- Maximum entropy
- Perturbative expansion
- Weighted trees