Complex-manifold (Kähler) structures for statistical models

Investigate the Fisher–Rao geometry of parametric statistical models M={p_θ: θ∈Θ} as complex manifolds when the model order is even, including the existence and properties of associated Kähler structures.

Background

The work suggests moving beyond real manifold structures to complex manifolds for even-dimensional models, motivated by connections to Kähler geometry and prior preliminary studies. Establishing a coherent complex (and potentially Kähler) geometric framework for Fisher–Rao manifolds could open new analytical tools and structural insights, complementing existing real and Hessian geometries.