Geometry of irregular statistical models

Study the differential-geometric structure of irregular statistical models for which the Fisher information matrix is not well-defined, including cases where the Fisher information is undefined or not positive-definite.

Background

The classical Fisher–Rao framework assumes regularity conditions ensuring a well-defined, positive-definite Fisher information matrix. Many practically relevant models violate these conditions. The paper points to Finsler geometry and Hellinger divergence as potential tools, but a general geometric theory for such irregular models remains undeveloped.