Related papers: Conditional Independence under Infinite Measures a…
Let $\sigma$ be a non-atomic, infinite Radon measure on $\mathbb R^d$, for example, $d\sigma(x)=z\,dx$ where $z>0$. We consider a system of freely independent particles $x_1,\dots,x_N$ in a bounded set $\Lambda\subset\mathbb R^d$, where…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
Two high-level "pictures" of probability theory have emerged: one that takes as central the notion of random variable, and one that focuses on distributions and probability channels (Markov kernels). While the channel-based picture has been…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
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…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
We define and study the independent natural extension of two local uncertainty models for the general case of infinite spaces, using the frameworks of sets of desirable gambles and conditional lower previsions. In contrast to Miranda and…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
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…
This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…
This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…
We study monotone and convex stochastic orders for processes with independent increments. Our contributions are twofold: First, we relate stochastic orders of the Poisson component to orders of their (generalized) L\'evy measures. The…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…