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Motivated by robustness studies under uncertainty of computer codes that simulate the behavior of a physical system, we are brought to inspect geodesic completeness of parametric families of truncated probability distributions. Specifically, we focus on the parametric family of truncated normal distributions with fixed truncation interval [a, b]. Endowed with the Fisher information metric, this family can be seen as a Riemannian manifold. We prove that it is not geodesically complete and conjecture a potential candidate for the completion.

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Geodesic Non-completeness of the Truncated Normal Family

  • 会议论文

  • 发表日期：

    2026年

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  • Baalu Belay Ketema,
  • Nicolas Bousquet,
  • Francesco Costantino,
  • Fabrice Gamboa,
  • Bertrand Iooss,
  • Roman Sueur

摘要

Motivated by robustness studies under uncertainty of computer codes that simulate the behavior of a physical system, we are brought to inspect geodesic completeness of parametric families of truncated probability distributions. Specifically, we focus on the parametric family of truncated normal distributions with fixed truncation interval [a, b]. Endowed with the Fisher information metric, this family can be seen as a Riemannian manifold. We prove that it is not geodesically complete and conjecture a potential candidate for the completion.