In this article, we evaluate the challenges and best practices associated with the Markov
bases approach to sampling from conditional distributions. We provide insights and …

In this work we investigate multipartition models, the subset of log-linear models for which
one can perform the classical iterative proportional scaling (IPS) algorithm to numerically …

In systems and synthetic biology, much research has focused on the behavior and design of
single pathways, while, more recently, experimental efforts have focused on how cross-talk …

Phylogenetic networks represent evolutionary histories of sets of taxa where horizontal
evolution or hybridization has occurred. Placing a Markov model of evolution on a …

The edges of any hypergraph parametrize a monomial algebra called the edge subring of
the hypergraph. We study presentation ideals of these edge subrings, and describe their …

The brain processes information about the environment via neural codes. The neural ideal
was introduced recently as an algebraic object that can be used to better understand the …

We study how to lift Markov bases and Gröbner bases along linear maps of lattices. We give
a lifting algorithm that allows to compute such bases iteratively provided a certain associated …

We study the maximum likelihood estimation problem for several classes of toric Fano
models. We start by exploring the maximum likelihood degree for all 2-dimensional …

Gaussian double Markovian models consist of covariance matrices constrained by a pair of
graphs specifying zeros simultaneously in the matrix and its inverse. We study the semi …

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 …