A fine-tuning measure is defined from the eigenvalues of a rescaled Fisher information matrix on parameter space, with a geometric interpretation as the pullback of the Euclidean metric from observable space.
Quantified naturalness from Bayesian statistics
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abstract
We present a formulation of naturalness made in the framework of Bayesian statistics, which unravels the conceptual problems related to previous approaches. Among other things, the relative interpretation of the measure of naturalness turns out to be unambiguously established by Jeffreys' scale. Also, the usual sensitivity formulation (so-called Barbieri-Giudice measure) appears to be embedded in our formulation under an extended form. We derive the general sensitivity formula applicable to an arbitrary number of observables. Several consequences and developments are further discussed. As a final illustration, we work out the map of combined fine-tuning associated to the gauge hierarchy problem and neutralino dark matter in a classic supersymmetric model.
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2026 1verdicts
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Naturalness and Fisher Information
A fine-tuning measure is defined from the eigenvalues of a rescaled Fisher information matrix on parameter space, with a geometric interpretation as the pullback of the Euclidean metric from observable space.