Dear all,
we are glad to announce the following seminar:
Speaker: professor Giovanni Pistone (de Castro Statistics, Collegio Carlo Alberto) Title: Affine Statistical Manifold: Finite State Space Date and time: Monday 28 november at 2 pm Place: room 508 at the Department of Mathematics, University of Genova YouTube channel: 508dima
Abstract: H. Weyl defines an affine space as a triple (M, V, ->), where V is a real vector space and M is a set with a binary external operation such that the parallelogram law holds. This notion was introduced in Relativity to derive simple notions of velocity and acceleration for curves in non-flat spaces. I have extended this setup to vector bundles to discuss the relevant affine geometries of the probability simplex. This type of study was called Information Geometry by S-i Amari. Especially, Amari and Nagaoka introduced a crucial notion of duality between mixture families and exponential families. J. Aitchinson developed a similar geometrical treatment of what he calls Statistics of Compositional Data. This affine setup is compatible but different with the metric set due to CR Rao and based on the observation that the Fisher information matrix of a statistical model defines a Riemannian metric on the probability simplex. A previous lecture on similar topics is transcribed at http://www.j-npcs.org/online/vol2020/v23no2p221.pdf. The present lecture is based on the material taken from https://arxiv.org/abs/2204.00917, https://www.mdpi.com/1099-4300/20/2/139, and https://arxiv.org/abs/1502.06718.https://arxiv.org/abs/1502.06718 The continuous case, not treated here, requires particular technical notions of differential geometry and functional analysis. See a summary at https://arxiv.org/abs/2210.07641
The seminar will be held in person and online via the YouTube channel: 508dima.
Best regards, Fabio Rapallo
-------------- Fabio Rapallo Dipartimento di Economia Universita' di Genova