We present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its... Show moreWe present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its Pearsonian analogue. Algebraically, this corresponds to deformations of toric ideals associated with graphs. Our discussion of the statistical issues centers around maximum likelihood estimation. Show less
The points of a moment variety are the vectors of all moments up to some order, for a given family of probability distributions. We study the... Show moreThe points of a moment variety are the vectors of all moments up to some order, for a given family of probability distributions. We study the moment varieties for mixtures of multivariate Gaussians. Following up on Pearson’s classical work from 1894, we apply current tools from computational algebra to recover the parameters from the moments. Our moment varieties extend objects familiar to algebraic geometers. For instance, the secant varieties of Veronese varieties are the loci obtained by setting all covariance matrices to zero. We compute the ideals of the 5-dimensional moment varieties representing mixtures of two univariate Gaussians, and we offer a comparison to the maximum likelihood approach. Show less
