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 models …

We study the maximum likelihood (ML) degree of linear concentration models in algebraic
statistics. We relate it to an intersection problem on the variety of complete quadrics. This …

We consider statistical models arising from the common set of solutions to a sparse
polynomial system with general coefficients. The maximum likelihood (ML) degree counts …

An important challenge in Geometric Modeling is to classify polytopes with rational linear
precision. Equivalently, in Algebraic Statistics one is interested in classifying scaled toric …

In this article, we introduce a new family of lattice polytopes with rational linear precision. For
this purpose, we define a new class of discrete statistical models that we call multinomial …

The linear optimization degree gives an algebraic measure of complexity of optimizing a
linear objective function over an algebraic model. Geometrically, it can be interpreted as the …

In this paper we propose a method that uses Lagrange multipliers and numerical algebraic
geometry to find all critical points, and therefore globally solve, polynomial optimization …

Many important problems in engineering are large scale and nonlinear--two things that are
inherently at odds. As a result, it is desirable to make use of underlying structure to reduce …

The Algebraic Statistics of Sampling, Likelihood, and Regression Page 1 The Algebraic
Statistics of Sampling, Likelihood, and Regression Der Fakultät für Mathematik und Informatik …

We study the maximum likelihood (ML) degree of linear concentration models in algebraic
statistics. We relate it to an intersection problem on the variety of complete quadrics. This …