Related papers: Bernoulli Randomness and Biased Normality

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

Let $X$, $B$ and $Y$ be three Dirichlet, Bernoulli and beta independent random variables such that $X\sim \mathcal{D}(a_0,...,a_d),$ such that $\Pr(B=(0,...,0,1,0,...,0))=a_i/a$ with $a=\sum_{i=0}^da_i$ and such that $Y\sim \beta(1,a).$ We…

We study a class of permutation tests of the randomness of a collection of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks of consecutive successes as overly representative of positive…

We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform…

As a fundamental piece of multi-object Bayesian inference, multi-object density has the ability to describe the uncertainty of the number and values of objects, as well as the statistical correlation between objects, thus perfectly matches…

We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This…

The duality $L^{\infty}\simeq (L^{1})'$ frequently breaks down in the presence of model uncertainty, where a single reference measure $P$ is replaced by a non-dominated family of probability measures $\mathcal{P}$. The unavailability of…

Let $\gamma_{n}= O (\log^{-c}n)$ and let $\nu$ be the infinite product measure whose $n$-th marginal is Bernoulli$(1/2+\gamma_{n})$. We show that $c=1/2$ is the threshold, above which $\nu$-almost every point is simply Poisson generic in…

Stern's diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of $2$ gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…

We introduce the twisted Bernoulli measures as a family of p-adic measures parametrized by the complement of the open disc with radius 1 and centered at 1 in the completion of an algebraic closure of p-adic numbers. These measures are the…

We investigate approximation of a Bernoulli partial sum process to the accompanying Poisson process in the non-i.i.d. case. The rate of closeness is studied in terms of the minimal distance in probability.

Let $s(n)$ denote the number of ones in the binary expansion of a natural number $n\in\mathbb{N}$. For any $t\in\mathbb{N}$ and $d\in\mathbb{Z}$, let $\mu_t(d)$ denote the asymptotic density of the set of those natural numbers $n$ for which…

This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…

We study the convergence of probability measures in terms of moments by applying operators to their Bessel generating functions. We consider a general setting of applying operators such as the Dunkl operator to formal power series that are…

Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…

Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope $\gamma-\epsilon$, where $\gamma$…

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…