On multivariable cumulant polynomial sequences with applications AS2015 Special Issue articles: This issue includes a series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics Conference held in Genoa, Italy, in June 2015. Special issue guest editors: Piotr Zwiernik and Fabio Rapallo. multi-index partition cumulant generating function formal power series Lévy process exponential model A new family of polynomials, called cumulant polynomial sequence, and its extension to the multivariate case is introduced relying on a purely symbolic combinatorial method. The coefficients are cumulants, but depending on what is plugged in the indeterminates, moment sequences can be recovered as well. The main tool is a formal generalization of random sums, when a not necessarily integer-valued multivariate random index is considered. Applications are given within parameter estimations, L ?evy processes and random matrices and, more generally, problems involving multivariate functions. The connection between exponential models and multivariable Sheffer polynomial sequences offers a different viewpoint in employing the method. Some open problems end the paper. Di Nardo, Elvira 2016 2016-07-12 Article application/pdf islandora:1007807 http://hdl.handle.net/10560/islandora:1007807 MATH / Applied Mathematics Illinois Institute of Technology Journal of Algebraic Statistics en Open Access