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The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test…
Change-point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large-scale, high-dimensional, and complex streaming data call for…
We study loss functions that measure the accuracy of a prediction based on multiple data points simultaneously. To our knowledge, such loss functions have not been studied before in the area of property elicitation or in machine learning…
Multi-user diversity is considered when the number of users in the system is random. The complete monotonicity of the error rate as a function of the (deterministic) number of users is established and it is proved that randomization of the…
The negative-binomial distribution is adopted for analyzing asbestos-fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers as well as the inevitable human variation in identifying and…
This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…
In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
This article provides some characterizations of extended COM-Poisson distribution: conditional distribution given the sum, functional operator characterization (Stein identity). We also give some conditions such that the extended…
Anomaly detection is the process of identifying cases, or groups of cases, that are in some way unusual and do not fit the general patterns present in the dataset. Numerous algorithms use discretization of numerical data in their detection…
The evaluation of a photon-pair source employs characteristic metrics like the photon-pair generation rate, heralding efficiency, and second-order correlation function, all of which are determined by the photon number distribution of the…
We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior distribution of the disorder time is known. The objective is…
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
We prove a Bernstein-type bound for the difference between the average of negative log-likelihoods of independent discrete random variables and the Shannon entropy, both defined on a countably infinite alphabet. The result holds for the…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
The problem of quickest detection of a change in the distribution of a sequence of random variables is studied. The objective is to detect the change with the minimum possible delay, subject to constraints on the rate of false alarms and…