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A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
In this paper, we investigate the problem of deciding whether two random databases $\mathsf{X}\in\mathcal{X}^{n\times d}$ and $\mathsf{Y}\in\mathcal{Y}^{n\times d}$ are statistically dependent or not. This is formulated as a hypothesis…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
For a zero-sum stochastic game which does not satisfy the Isaacs condition, we provide a value function representation for an Isaacs-type equation whose Hamiltonian lies in between the lower and upper Hamiltonians, as a convex combination…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a…
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a…
We here provide a distribution-free approach to the random factor analysis model. We show that it leads to the same estimating equations as for the classical ML estimates under normality, but more easily derived, and valid also in the case…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…
We study the asymptotic laws for the spatial distribution and the number of connected components of zero sets of smooth Gaussian random functions of several real variables. The primary examples are various Gaussian ensembles of real-valued…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
It is shown that the probabilities for the spin singlet can be reproduced through classical resources, with no communication between the distant parties, by using merely shared (pseudo-)randomness. If the parties are conscious beings aware…
This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…
Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…
In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs.…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…
Multivariate Gaussian distributions enjoy Gaussian conditional distributions that makes conditioning easy: conditioning boils down to implementing analytical formulae for conditional means and covariances. For more general distributions,…
When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when…