Roberto Fontana

Given an orthogonal array we analyze the aberrations of the sub-fractions which are obtained by the deletion of some of its points. We provide formulae to compute the Generalized Word-Length Pattern of any sub-fraction. In the case of the deletion of one single point, we provide a simple methodology to find which the best sub-fractions are according to the Generalized Minimum Aberration criterion.

We provide sharp analytical upper and lower bounds for value-at-risk (VaR) and sharp bounds for e...xpected shortfall (ES) of portfolios of any dimension subject to default risk.

We propose a simple but new method of characterizing multivariate Bernoulli variables belonging to a given class, i.e., with some specified moments. Within a given class, this characterization allows us to generate easily a sample of mass functions. It also provides the bounds that all the moments must satisfy to be compatible and the possibility to choose the best distribution according to a certain criterion. For the special case of the Fréchet class of the multivariate Bernoulli distributions with given margins, we find a polynomial characterization of the class.

An algorithm for the creation of mixed level arrays with generalized minimum aberration (GMA) is proposed. GMA mixed level arrays are particularly useful for experiments involving qualitative factors: for these, the number of factor levels is often a consequence of subject matter requirements, while a priori assumptions on a statistical model are not made, apart from assuming lower order effects to be more important than higher order effects. The proposed algorithm creates GMA arrays using mixed integer optimization with conic quadratic constraints.

Algebraic sampling methods are a powerful tool to perform hypothesis testing for non-negative discrete exponential families, when the exact computation of the test statistic null distribution is computationally infeasible. We propose an improvement of the accelerated sampling described by Diaconis and Sturmfels (1998) based on permutations. We thus establish a link between standard permutation and algebraic-statistics-based sampling.

This paper applies probabilistic graphical models in a new framework to study association rules driven by consumer choices in a network of Italian museums. The network consists of the museums participating in the programme of Abbonamento Musei Torino Piemonte, which is a yearly subscription managed by Associazione Torino Città Capitale Europea. It is available to people living in the Piemonte region, Italy. Consumers are card-holders, who are allowed entry to all the museums in the network for one year.