Date & Time: Wednesday, April 09, 2014, 14:30-15:30.
Venue: Ramanujan Hall
Speaker: Michel Nguiffo Boyom, Université Montpellier 2
Title: A functional characteristic invariant for global statistical models for a measurable set
Abstract: In the literature a q-dimensional statistical model for a measurable set is a q-dimensional open manifold admitting an embedding in the q-dimensional euclidian space. As is implicitly suggested in Amari-Nagaoka monograph - "Methods of information geometry" - this restriction is caused by nonessential diffculties such as the need of global coordinate functions. Another remark is that many compact manifolds may be excluded. The aim of the talk is to present a new definition of statistical models from the viewpoint of locally trivial fibration. A combination of Hessian geometry together with this viewpoint yield a map Q of the set of symmetric linear gauges in the set of random Hessian metrics. The map Q determines the model up to diffeormorphism. The mathematical expectation of Q is the Fisher information of the model.