**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.