Related papers: Poisson-process limit-laws yield Gumbel Max-Min an…
We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…
We establish sufficient conditions for the Marcinkiewicz-Zygmund type weak law of large numbers for a linear process $\{X_k:k\in\mathbb Z\}$ defined by $X_k=\sum_{j=0}^\infty\psi_j\varepsilon_{k-j}$ for $k\in\mathbb Z$, where…
The greatest root statistic arises as the test statistic in several multivariate analysis settings. Suppose there is a global null hypothesis that consists of different independent sub-null hypotheses, and suppose the greatest root…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…
In weakest link models the failure of a single microscopic element of a brittle material causes the failure of an entire macroscopic specimen, just as a chain fails if one link fails. Pristine samples of glass, such as optical…
We prove that the extremal process of branching Brownian motion, in the limit of large times, converges weakly to a cluster point process. The limiting process is a (randomly shifted) Poisson cluster process, where the positions of the…
Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding parameters. This…
Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…
Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational optimization to complex networks. They are often approached using random matrices with Poisson-distributed or…
The missing data problem pervasively exists in statistical applications. Even as simple as the count data in mortality projections, it may not be available for certain age-and-year groups due to the budget limitations or difficulties in…
We study a supply chain consisting of production-inventory systems at several locations which are coupled by a common supplier. Demand of customers arrives at each production system according to a Poisson process and is lost if the local…
The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures~(CRM)…
Extreme values are considered in samples with random size that has a mixed Poisson distribution being generated by a doubly stochastic Poisson process. We prove some inequalities providing bounds on the rate of convergence in limit theorems…
In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…
Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…
Space debris is a major problem in space exploration. International bodies continuously monitor a large database of orbiting objects and emit warnings in the form of conjunction data messages. An important question for satellite operators…
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…
We give a sufficient condition for a random sequence in [0,1] generated by a $\Psi$-process to be equidistributed. The condition is met by the canonical example -- the $\max$-2 process -- where the $n$th term is whichever of two uniformly…
We consider a matching system where items arrive one by one at each node of a compatibility network according to Poisson processes and depart from it as soon as they are matched to a compatible item. The matching policy considered is a…
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct…