( ) 1–1–1 2 The National Institute of Advanced Industrial Science and Technology, Central 2, 1–1–1 Umezono Tsukuba-shi Ibaraki 305–8568, Japan E-mail: s.akaho@aist.go.jp differential geometry duality flat space projection probabilistic model statistical inference JL 002/02/4202–0086 c �2002 SICE 1. 1 ˆ ξ1 ξ2 1 2. 2.1 n ξ = (ξ1 , . . . , ξn ) X f(x; ξ) 1 ξ 1 ( ) X {x0, x1, . . . , xn} Prob(X = xi) =