Related papers: The Geometry of Statistical Models for Two-Way Con…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
In a two-way contingency table analysis with explanatory and response variables, the analyst is interested in the independence of the two variables. However, if the test of independence does not show independence or clearly shows a…
Motivated by applications to perverse sheaves, we study combinatorics of two cell decompositions of the symmetric product of the complex line, refining the complex stratification by multiplicities. Contingency matrices, appearing in…
Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the table. While classical results show that…
In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distribution of the crossing numbers of such random knots. We also…
We revisit the geometrical meaning of statistical isotropy that is manifest in excursion sets of smooth random fields in two dimensions. Using the contour Minkowski tensor, $\W_1$, as our basic tool we first examine geometrical properties…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
In a recent series of papers [1--3], a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data.…
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
We present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its Pearsonian analogue. Algebraically, this corresponds to deformations of toric ideals associated…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
Let $\mathbf{T}_{\mathbf{a},\mathbf{b}}$ be the number of $3$-way contingency tables of size $m \times n \times p$ with two of its three plane-sum margins fixed by $\mathbf{a}=(a_1, \ldots, a_m) \in \mathbb{N}^m$ and $\mathbf{b}=(b_1,…
The need for statistical models of orientations arises in many applications in engineering and computer science. Orientational data appear as sets of angles, unit vectors, rotation matrices or quaternions. In the field of directional…
We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting that have constant failure rate. In spite of the minimal algebraic structure, there is a…
Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied…
Square contingency tables are traditionally analyzed with a focus on the symmetric structure of the corresponding probability tables. We view probability tables as elements of a simplex equipped with the Aitchison geometry. This perspective…
We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…