Related papers: No eleventh conditional Ingleton inequality

U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\theta(P_{X})$ of…

Conditional models with one pair of conditional and conditioned factors in Mukerjee et al. (2017) are extended to two pairs in this paper. The extension includes the parametrization, effect hierarchy, sufficient conditions for universal…

In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…

Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…

A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of…

Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…

We study the problem of testing the null hypothesis that X and Y are conditionally independent given Z, where each of X, Y and Z may be functional random variables. This generalises testing the significance of X in a regression model of…

Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs…

In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…

Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…

The asymptotic freeness of independent unitarily invariant $N\times N$ random matrices holds in expectation up to $O(N^{-2})$. An already known consequence is the infinitesimal freeness in expectation. We put in evidence another consequence…

This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…

This paper examines the biases and performance of several uncertain inference systems: Mycin, a variant of Mycin. and a simplified version of probability using conditional independence assumptions. We present axiomatic arguments for using…

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different…

We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new…

We study an information analogue of infinitely divisible probability distributions, where the i.i.d. sum is replaced by the joint distribution of an i.i.d. sequence. A random variable $X$ is called informationally infinitely divisible if,…

Any unconstrained information inequality in three or fewer random variables can be written as a linear combination of instances of Shannon's inequality I(A;B|C) >= 0 . Such inequalities are sometimes referred to as "Shannon" inequalities.…

Let $X$ be a max-stable random vector with positive continuous density. It is proved that the conditional independence of any collection of disjoint sub-vectors of $X$ given the remaining components implies their joint independence. We…

We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…