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In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation…
A protocol for distributed estimation of discrete distributions is proposed. Each agent begins with a single sample from the distribution, and the goal is to learn the empirical distribution of the samples. The protocol is based on a simple…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The…
Posterior distribution over a countable set M of continuous data-sampling distributions piles up at L-projection of the true distribution r on M, provided that the L-projection is unique. If there are several L-projections of r on M, then…
We consider the problem of classification of points sampled from an unknown probability measure on a Euclidean space. We study the question of querying the class label at a very small number of judiciously chosen points so as to be able to…
This study developed a new statistical model and method for analyzing the precision of binary measurement methods from collaborative studies. The model is based on beta-binomial distributions. In other words, it assumes that the sensitivity…
As a part of our works on effective properties of probability distributions, we deal with the corresponding characteristic functions. A sequence of probability distributions is computable if and only if the corresponding sequence of…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
Many forecasting applications have a limited distributed target variable, which is zero for most observations and positive for the remaining observations. In the econometrics literature, there is much research about statistical model…
A Bayesian approach to variable selection which is based on the expected Kullback-Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. Here we extend this idea by…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
In this paper we describe a probabilistic method for estimating the position of an object along with its covariance matrix using neural networks. Our method is designed to be robust to outliers, have bounded gradients with respect to the…
How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation,…
The paper deals with three generalized dependent setups arising from a sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these…
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties…
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…