Decomposable (probabilistic) models are log-linear models generated by acyclic hypergraphs, and a number of nice properties enjoyed by them are known. In many applications the following selection problem naturally arises: given a probability distribution $p$ over a finite set $V$ of $n$ discrete variables and a positive integer $k$, find a decomposable model with tree-width $k$ that best fits $p$. If $\mathscr{H}$ is the generating hypergraph of a decomposable model and $p_{\mathscr{H}}$ is the estimate of $p$ under the model, we can measure...

Dans cet article, nous présentons une démarche d'analyse statistique d'un questionnaire appliquée à une enquête sur le racisme. La méthodologie suivie est celle de l'ana lyse des données structurées, inspirée des comparaisons spécifiques en analyse de variance, et appliquée à des données géométriques (nuage euclidien). La mise en œuvre est réalisée grâce au langage d'interrogation de données (LID) implanté dans le logiciel EyeLID.

In this paper, we characterise and classify a list of full conditional independences via the structure of the induced set of vanishing atoms. Construction of Markov random subfield and minimal characterisation of polymatroids satisfying a MRF will also be given.

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

Given a fixed dependency graph $G$ that describes a Bayesian network of binary variables $X_1,\cdots ,X_n$, our main result is a tight bound on the mutual information $I_c(Y_1,\cdots ,Y_k)={\sum }_{j=1}^{k}H\left(Y_j\right)/c-H(Y_1,\cdots ,Y_k)$ of an observed subset $Y_1,\cdots ,Y_k$ of the variables $X_1,\cdots ,X_n$. Our bound depends on certain quantities that can be computed from the connective structure of the nodes in $G$. Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.

Outlier robust diagnostics (graphically) using Robustly Studentized Robust Residuals (RSRR) and Partial Robustly Studentized Robust Residuals (PRSRR) are established. One problem with some robust residual plots is that the residuals retain information from certain predicated values (Velilla, 1998). The RSRR and PRSRR techniques are unaffected by this complication and as a result they provide more interpretable results.

The sum-product algorithm is a well-known procedure for marginalizing an “acyclic” product function whose range is the ground set of a commutative semiring. The algorithm is general enough to include as special cases several classical algorithms developed in information theory and probability theory. We present four results. First, using the sum-product algorithm we show that the variable sets involved in an acyclic factorization satisfy a relation that is a natural generalization of probability-theoretic...

Le stéréogramme de liaison est une représentation graphique simultanée de la distribution conjointe de deux variables ordonnées, de leurs distributions marginales, et de la densité de la première par rapport au produit des deux autres. On y lit une forme de liaison statistique qui est introduite sous le nom de liaison blackienne et dont on discute les rapports avec la liaison stochastique.