Details:
Title  Cumulant varieties  Author(s)  Giovanni Pistone, Henry P. Wynn  Type  Article in Journal  Abstract  For a discrete distribution in R d on a finite support D probabilities and moments are algebraically related. If there are n =  D  support points then there are n probabilities p ( x ) , x ∈ D and n basic moments. By suitable interpolation of the probabilities using a Gröbner basis method, high order moments can be express linearly in terms of n basic moments. A main result is that high order cumulants can also be expressed as polynomial functions of n low order moments and cumulants. This means that statistical models which can be expressed via an algebraically variety for the basic probabilities and moments, such as graphical models, induce a variety for the basic cumulants, which we shall call the “cumulant variety”. It is important to stress that the cumulant variety depends on the monomial ordering defining the original Gröbner basis.  Keywords  Probability, Moments, Cumulants, Variety, Ideal, Gröbner bases  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717105001161 
Language  English  Journal  Journal of Symbolic Computation  Volume  41  Number  2  Pages  210  221  Year  2006  Note  Computational Algebraic Statistics Computational Algebraic Statistics  Edition  0  Translation 
No  Refereed 
No 
