Sections / Section 6: Information Geometry and Cumulant Tower / bhattacharyyaCoeff

Bhattacharyya Coeff

defprovedInfo Geometry

Documentation

Lean 4 Proof

def bhattacharyyaCoeff {J : ℕ} (s0 s1 : Fin J → ℝ) : ℝ :=
  ∑ j : Fin J, Real.sqrt (s0 j * s1 j)

Dependency Graph

Used by

bhattacharyya_uniform_self fisherRao_distance_invariance fisherRaoDistance bhattacharyya_eq_cos_distance fisherRaoDistance_self

Location

thesis/CESProofs/Foundations/InformationGeometry.lean:408

Module Section

Information Geometry of CES:

In the same file

bregmanDiv welfare_eq_bregman klDivExp welfare_eq_kl kl_reverse welfareDistanceFn_deriv welfareDistanceFn_second_deriv fisherInfoExp welfare_curvature_is_fisher hessLogFEigenvalue hessLogF_from_cesEigenvalue escortFisherEigenvalue bridgeRatio bridge_theorem curvatureK_eq_bridge_times_fisher curvatureK_from_hessLogF fifth_role_of_K hierarchical_kl bridgeRatio_pos bridgeRatio_large_at_small_rho