We introduce a new indicator for dynamical systems, namely the averaged number of visits, to estimate the frequency of visits in small regions when a map is iterated up to the inverse of the measure of this region. We compute this quantity analytically and numerically for various systems and we show that it depends on the ergodic properties of the systems and on their topological properties, su...

Most real-world data is stored in relational form. In contrast, most statistical learning methods work with “flat” data representations, forcing us to convert our data into a form that loses much of the relational structure. The recently introduced framework of Probabilistic Relational Models (PRMs) allows us to represent probabilistic models over multiple entities that utilize the relations be...

We develop averaged instrumental variables estimators as a way to deal with many weak instruments. We propose a weighted average of the preliminary k-class estimators, where each estimator is obtained using different subsets of the available instrumental variables. The averaged estimators are shown to be consistent and to satisfy asymptotic normality. Furthermore, its approximate mean squared e...

A statistical mechanics description of complex molecular systems involves the determination of ensembles of conformations that represent their Boltzmann distributions. The observable properties of these systems can be then predicted by calculating averages over such ensembles. In principle, given accurate energy functions and efficient sampling methods, these ensembles can be generated by molec...

In this paper, we present a shared frailty model for gap time distributions of recurrent event data with competing risks based on weighted risk-set method. The parameters the are estimated using EM algorithm. A simulation study is carried out to assess performance proposed estimators. An application illustrated real life set.

Computational fluid dynamics using the Reynolds-averaged Navier–Stokes (RANS) remains most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are biggest sources of errors uncertainties model predictions. This work aims quantify model-form RANS simulations farms at high Reynolds numbers under neutrally strat...