Related papers: Conditional negative association for competing urn…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
The conditional randomization test (CRT) was recently proposed to test whether two random variables X and Y are conditionally independent given random variables Z. The CRT assumes that the conditional distribution of X given Z is known…
Assume that $2n$ balls are thrown independently and uniformly at random into $n$ bins. We consider the unlikely event $E$ that every bin receives at least one ball, showing that $\Pr[E] = \Theta(b^n)$ where $b \approx 0.836$. Note that, due…
The multiple testing literature has primarily dealt with three types of dependence assumptions between p-values: independence, positive regression dependence, and arbitrary dependence. In this paper, we provide what we believe are the first…
A common form of competition is one where judges grade contestants' performances which are then compiled to determine the final ranking of the contestants. Unlike in another common form of competition where two contestants play a…
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…
An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the…
A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i \to…
In this paper we study records obtained from partial comparisons within a sequence of independent and identically distributed (i.i.d.) random variables, indexed by positive integers, with a common density~\(f.\) Our main result is that if…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
The challenge of understanding the collective behaviors of social systems can benefit from methods and concepts from physics [1-6], not because humans are similar to electrons, but because certain large-scale behaviors can be understood…
In this paper, lower bounds on the probability of a finite union of events are considered, i.e. $P\left(\bigcup_{i=1}^N A_i\right)$, in terms of the individual event probabilities $\{P(A_i), i=1,\ldots,N\}$ and the sums of the pairwise…
By jagged partitions we refer to an ordered collection of non-negative integers $(n_1,n_2,..., n_m)$ with $n_m\geq p$ for some positive integer $p$, further subject to some weakly decreasing conditions that prevent them for being genuine…
We study a P\'olya-type urn model defined as follows. Start at time 0 with a single ball of some colour. Then, at each time n>0, choose a ball from the urn uniformly at random. With probability 1/2<p<1, return the ball to the urn along with…
We present a multiple colour generalisation of the model of graph interacting urns studied by Benaim et. al., Random Struct. Alg., 46: 614-634, 2015. We show that for complete graphs and for a broad class of reinforcement functions…
Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…
We provide a complete characterisation of the phenomenon of adversarial examples - inputs intentionally crafted to fool machine learning models. We aim to cover all the important concerns in this field of study: (1) the conjectures on the…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…
We establish a sharp moment comparison inequality between an arbitrary negative moment and the second moment for sums of independent uniform random variables, which extends Ball's cube slicing inequality.
Mason's Conjecture asserts that for an $m$--element rank $r$ matroid $\M$ the sequence $(I_k/\binom{m}{k}: 0\leq k\leq r)$ is logarithmically concave, in which $I_k$ is the number of independent $k$--sets of $\M$. A related conjecture in…