Abstract
July 1 - 15.20-15.50
G.Pistone
- Recent Results on Exponential Statistical Manifolds
In a paper published 1995 with C. Sempi, a definition of the manifold
structure of the positive probability densities was introduced. Such
manifold in modeled on Orlicz spaces with exponential Young function
and is based on the representation of probabilities as non-parametric
exponential models. The idea was further developed in a paper with
M.-P. Rogantin (1999) with improvement of the basic contruction and a
few results on the expectation parameterization on submanifolds. the
theory is still lacking of important features and the basic approach,
eg the use of Banach space of Orlicz type as local models in the
framework of standard manifold theory has been questioned.
On the positive side, a number of new results has been derived
recently and old results have been improved: it is expected that some
of these improvement will be presented by the author during the
meeting.
We will give a short presentation of the basic theory as we know it
now, recalling what it is already known and adding the new features,
expecially on the regularity of change of coordinates, cumulant
function, submanifolds, alternative structures. Other important
chapters, eg the theory on the tangent bundle with submanifolds and
connections, or the relation with information theory will be presented
by other authors.
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