Related papers: Random Monomial Ideals Macaulay2 Package
Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to…
We characterize monomial ideals which are intersections of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
This paper studies the numbers of minimal generators of powers of monomial ideals in polynomial rings. For a monomial ideal $I$ in two variables, Eliahou, Herzog, and Saem gave a sharp lower bound $\mu (I^2)\ge 9$ for the number of minimal…
In this paper, we present Insertus.jl, the Julia package that can help the user generate a randomization sequence of a given length for a multi-arm trial with a pre-specified target allocation ratio and assess the operating characteristics…
We consider the problem of determining whether a monomial ideal is dominant. This property is critical for determining for which monomial ideals the Taylor resolution is minimal. We first analyze dominant ideals with a fixed least common…
The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead,…
We study when Taylor resolutions of monomial ideals are minimal. We consider monomial ideals with linear quotients. In particular, we determine precisely the stable ideals and the monomial ideals with linear resolutions having the miminal…
Structural Equation Modeling (SEM) is an umbrella term that includes numerous multivariate statistical techniques that are employed throughout a plethora of research areas, ranging from social to natural sciences. Until recently, SEM…
This article highlights the ToricHigherDirectImages package in Macaulay2. The central feature is a method for computing (higher) direct images of line bundles under surjective toric morphisms.
The random-effects or normal-normal hierarchical model is commonly utilized in a wide range of meta-analysis applications. A Bayesian approach to inference is very attractive in this context, especially when a meta-analysis is based only on…
In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simplicial complexes and random clique complexes as special…
dynamite is an R package for Bayesian inference of intensive panel (time series) data comprising multiple measurements per multiple individuals measured in time. The package supports joint modeling of multiple response variables,…
Random variables and their distributions are a central part in many areas of statistical methods. The Distributions.jl package provides Julia users and developers tools for working with probability distributions, leveraging Julia features…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…
We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical…
We compute some algebraic invariants (e.g. depth, Castelnuovo - Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products.
In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems…
Proofs of two results about a monomial ideal -- describing membership in auxiliary ideals associated to the monomial ideal -- are given which do not invoke resolution of singularities. The AM--GM inequality is used as a substitute for…
We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals…