Paper shows bounded approximations for Fisher-Rao distance in parametric models
FrnkNlsn · x · 2026-07-24
A paper on Fisher-Rao distances proposes numerically robust approximation and bounding methods for parametric statistical models.
- The paper notes that Fisher-Rao distance is not known in closed form for multivariate normals, but can be approximated arbitrarily finely with guaranteed lower and upper bounds.
- It reviews generic upper bounds, approximation schemes depending on whether geodesics or pregeodesics are available in closed form, and methods that can guarantee arbitrarily small additive error.
- For models whose Fisher metric is a Hessian metric, it derives generic tight upper bounds on Fisher-Rao distances as square roots of Jeffreys–Bregman divergences.
- It also extends the approach to elliptical distribution families and proposes new distances based on Fisher-Rao lengths of curves as proxies for the exact geodesic distance.
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