Search

Workshop

Finite generation of cumulants

  • Giovanni Pistone (Collegio Carlo Alberto, Moncalieri, Italy)
University n.n. Universität Leipzig (Leipzig)

Abstract

In case of a finite state space, we can analyze statistical exponential families with tools from both Differential Geometry and Commutative Algebra, see e.g. Gibilisco, Riccomagno, Rogantin, Wynn eds (2009). A key feature of the algebraic framework is the finite generation of polinomial ideals. In the general case, the reduction to some sort of finite generation is more difficult, but it is a classical ingredient of standard statistical models. We suggested in Pistone and Wynn Statistica Sinica (1999) a definition of finite generation which is a generalization of the Morris class of distribution, see Morris Annals of Statistics (1982, 1983). We present here a development of this theory which makes use of recent results on Gröbner bases for D-modules. This is a joint work with Henry Wynn, LSE London UK.

Links

conference
02.08.10 06.08.10

Information Geometry and its Applications III

Universität Leipzig University n.n.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences, Germany

Paolo Gibilisco

Università degli Studi di Roma "Tor Vergata", Italy

František Matúš

Academy of Sciences of the Czech Republic, Czech Republic