9 citations · 23 across the 6 of their papers we have counts for
10 papers
Differential Equations for Gaussian Statistical Models with Rational Maximum Likelihood Estimator
Carlos Améndola, Lukas Gustafsson, Kathlén Kohn +2
We study multivariate Gaussian statistical models whose maximum likelihood estimator (MLE) is a rational function of the observed data. We establish a one-to-one correspondence bet…
Classifying one-dimensional discrete models with maximum likelihood degree one
Arthur Bik, Orlando Marigliano
We propose a classification of all one-dimensional discrete statistical models with maximum likelihood degree one based on their rational parametrization. We show how all such mode…
Coloured Graphical Models and their Symmetries
Isobel Davies, Orlando Marigliano
Coloured graphical models are Gaussian statistical models determined by an undirected coloured graph. These models can be described by linear spaces of symmetric matrices. We outli…
The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices
Carlos Améndola, Lukas Gustafsson, Kathlén Kohn +2
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is,…
The curved exponential family of a staged tree
Christiane Görgen, Manuele Leonelli, Orlando Marigliano
Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic…
Multivariate boundary regression models
Leonie Selk, Charles Tillier, Orlando Marigliano
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general Hölder class and estimate it via a nonpar…
Maximum likelihood degree of the two-dimensional linear Gaussian covariance model
Jane Ivy Coons, Orlando Marigliano, Michael Ruddy
In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this nu…
Discrete Statistical Models with Rational Maximum Likelihood Estimator
Eliana Duarte, Orlando Marigliano, Bernd Sturmfels
A discrete statistical model is a subset of a probability simplex. Its maximum likelihood estimator (MLE) is a retraction from that simplex onto the model. We characterize all mode…
Random points on an algebraic manifold
Paul Breiding, Orlando Marigliano
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for compu…
Verlinde bundles of families of hypersurfaces and their jumping lines
Orlando Marigliano
Verlinde bundles are vector bundles arising as the direct image of polarizations of a proper family of schemes . We s…