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Evidence integrals. (English) Zbl 0895.94006
Hanson, Kenneth M. (ed.) et al., Maximum entropy and Bayesian methods. Proceedings of the 15th international workshop, Santa Fe, NM, USA, July 31–August 4, 1995. Dordrecht: Kluwer Academic Publishers. Fundam. Theor. Phys. 79, 443-448 (1996).
Summary: Evidence integrals are a key ingredient of quantified maximum entropy (QME). They allow to evaluate hyper-parameters which in turn determine the amount of regularization, the noise level, confidence intervals etc. Consequently, the exact evaluation of these multidimensional integrals is of central importance to the theory. Since the conventional ‘steepest descent’ (SD) approximation fails frequently a more refined approach is needed. Using diagrammatic techniques we derive a correction factor to the SD result which is readily incorporated in existing QME codes and which provides significantly improved results.
For the entire collection see [Zbl 0855.00029].
94A17 Measures of information, entropy
65D30 Numerical integration
62A01 Foundations and philosophical topics in statistics
62B10 Statistical aspects of information-theoretic topics