Related papers: Marginal Independence and Partial Set Partitions
The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…
We study two partial orders on $[x_1,...,x_n]$, the free abelian monoid on ${x_1,...,x_n}$. These partial orders, which we call the ``strongly stable'' and the ``stable'' partial order, are defined by the property that their filters are…
We provide a differential-algebraic description of forking independence in the stable theory DCF$_{p,m}$ of differentially closed fields of characteristic $p>0$ with $m$-many commuting derivations. As a by-product of this description, we…
Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix…
We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular,…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
We introduce and study the property of orthogonal independence, a restricted additivity axiom applying when alternatives are orthogonal. The axiom requires that the preference for one marginal change over another should be maintained after…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
Each partition $\lambda = (\lambda_1, \lambda_2, ..., \lambda_n)$ determines a so-called Ferrers tableau or, equivalently, a Ferrers bipartite graph. Its edge ideal, dubbed Ferrers ideal, is a squarefree monomial ideal that is generated by…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics. We show that common desirable…
Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a…
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, mor-phisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives…
We introduce a new stochastic order for the tail dependence between random variables. We then study different measures of tail dependence which are monotone in the proposed order, thereby extending various known tail dependence coefficients…
Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…
In this paper we study a new class of statistical models for contingency tables. We define this class of models through a subset of the binomial equations of the classical independence model. We use some notions from Algebraic Statistics to…
A non-trivial topological group is called \emph{$d$-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting it trivially. This notion was introduced by M\'arquez and…
The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…