The algebra of interpolatory cubature formulae for generic nodes
  We consider the classical problem of computing the expected value of a real function $f$ of the $d$-variate random variable $X$ using cubature formul\ae. We use in synergy tools from Commutative Algebra for cubature rul\ae, from elementary orthogonal polynomial theory and from Probability. 
Claudia Fassino, Giovanni Pistone and Eva Riccomagno
math.ST math.AC stat.TH