Limits of exponential models on a lattice
Giovanni Pistone · 2004
The term “Algebraic Statistics” (AS) was introduced in Pistone et al. (2001) to denote the use in Statistics of mathematical technologies taken from Computational Commutative Algebra (CCA). The subject, started as early as 1993 in a preprint of the seminal paper Diaconis and Sturmfels (1998), is currently under intensive development; the best description of the current state of the art is obtained by looking at the papers and discussion presented in the specialized workshops: GrostatVI3, Menton Fr 2003, Computational Algebraic Statistics4, AIM Palo Alto Ca 2003, Computational Algebra for Algebraic Geometry and Statistics5, Torino It 2004. We cannot include in this short note an extensive bibliography. A very active area of development consists of the exploration of multiple application of algebraic computations to graphical models. The present paper illustrate the matter through a specific example, the 4-cycle as described in Lauritzen (1996). Two of the results below are published here, in short form, for the first time. Preliminary versions were published in Rapallo (2003) and Pistone and Wynn (2003). related results with full proofs are in Rapallo (2004). The present research is joint work with Fabio Rapallo and Henry P. Wynn. At the Conference time, all relevant computer listings and results will be posted on the Author’s web-site6.