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We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…

Individuals have an intuitive perception of what makes a good coincidence. Though the sensitivity to coincidences has often been presented as resulting from an erroneous assessment of probability, it appears to be a genuine competence,…

Within the setting of rare event modelling, the method of level sets allows us to define an equivalence relation over rare events with distinct rates of entropy production. This method allows us to clarify the relation between the empirical…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

We prove that for every $\epsilon>0$ there exists $\delta>0$ such that the following holds. Let $\mathcal{C}$ be a collection of $n$ curves in the plane such that there are at most $(\frac{1}{4}-\epsilon)\frac{n^{2}}{2}$ pairs of curves…

This paper considers ranking inference of $n$ items based on the observed data on the top choice among $M$ randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for $M$-way ranking with only the top…

A sequence of graphs is FO-convergent if the probability of satisfaction of every first-order formula converges. A graph modeling is a graph, whose domain is a standard probability space, with the property that every definable set is Borel.…

Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…

Consider the binomial model $G^{d+1}(n,p)$ of the random $(d+1)$-uniform hypergraph on $n$ vertices, where each edge is present, independently of one another, with probability $p:\mathbb{N}\to[0,1]$. We prove that, for all…

In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…

We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently describe a broad class of random tilings models,…

Let A_1,...,A_k be a collection of families of subsets of an n-element set. We say that this collection is cross-intersecting if for any i,j in [k] with i not equal to j, A in A_i and B in A_j implies that the intersection of A and B is…

We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…

Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…

Let $\prec$ be the product order on $\mathbb{R}^k$ and assume that $X_1,X_2,\ldots,X_n$ ($n\geq3$) are i.i.d. random vectors distributed uniformly in the unit hypercube $[0,1]^k$. Let $S$ be the (random) set of vectors in $\mathbb{R}^k$…

For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…

Let $A^{(n)}_{l;k}\subset S_n$ denote the event that the set of $l$ consecutive numbers $\{k,k+1,\cdots, k+l-1\}$ appear in a set of $l$ consecutive positions. Let $p=\{p_j\}_{j=1}^\infty$ be a distribution on $\mathbb{N}$ with $p_j>0$. Let…

The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…

Let $\mathcal{M}$ be a set with $M$ elements, let $\psi :\mathcal{M}\to\mathcal{M}$ be a bijective involution, and let~$\boldsymbol{\mathcal{X}}_{\psi}$ be the set of sequences $(x_1,\dots,x_M)\in\mathcal{M}^M$ with the property that…

We build on the classification in [1] of event sequences in the influence network as respecting collinearity or not, so as to determine in future work what phenomena arise in each case. Collinearity enables each observer to uniquely…