Related papers: A method for Sampling Bernoulli Variables
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
By applying Sklar's theorem to the Multivariate Bernoulli Distribution (MBD), this paper proposes a framework to decouple marginal distributions from the dependence structure, clarifying interactions among binary variables. Explicit…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfying moment conditions, we use the generating function of these…
We consider the problem of computing with many coins of unknown bias. We are given samples access to $n$ coins with \emph{unknown} biases $p_1,\dots, p_n$ and are asked to sample from a coin with bias $f(p_1, \dots, p_n)$ for a given…
We say that a random integer variable $X$ is monotone if the modulus of the characteristic function of $X$ is decreasing on $[0,\pi]$. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random…
We extend some equatilites in the Owen's table of normal integrals (A table of normal integrals in Communication in Statistics-Simulation and Computation, 1980). Furthermore a new probabilistic model for a vector of binary random variables…
We propose a new method to construct a stationary process and random field with a given decreasing covariance function and any one-dimensional marginal distribution. The result is a new class of stationary processes and random fields. The…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two…
We leverage proof techniques Fourier analysis and an existing result in coding theory to derive new bounds for the problem of non-interactive simulation of binary random variables. Previous bounds in the literature were derived by applying…
In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the acceptance-rejection method, and it is particularly useful for kinetic…
In this paper, an analysis of the undetected error probability of ensembles of binary matrices is presented. The ensemble called the Bernoulli ensemble whose members are considered as matrices generated from i.i.d. Bernoulli source is…
Clinical trials often evaluate multiple outcome variables to form a comprehensive picture of the effects of a new treatment. The resulting multidimensional insight contributes to clinically relevant and efficient decision-making about…
We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…
We explore the class of exchangeable Bernoulli distributions building on their geometrical structure. Exchangeable Bernoulli probability mass functions are points in a convex polytope and we have found analytical expressions for their…
We study the local limit theorem for weighted sums of Bernoulli variables. We show on examples that this is an important question in the general theory of the local limit theorem, and which turns up to be not well explored. The examples we…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
Let $\BS_1,...,\BS_n$ be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter $p\in(0,1)$. Let $m_*(p):=(1+p+2p^2)/(2\sqrt{p-p^2}+4p^2)$ if $0<p\le 1/2$ and $m_*(p):=1$ if…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, thus simple models exhibiting some…