Veranstaltungen

We revisit the classic simple symmetric exclusion process, which has the same hydrodynamic limit as a system of independent random walkers. Our aim is to provide a deeper understanding why the exclusion mechanism does not influence the hydrodynamic limit. We do this by interpreting each time the exclusion mechanism is invoked as a collision between particles, then keep track of the number of collisions in the system and pass to the hydrodynamic limit. In fact we study four of such variables under different scaling regimes and obtain a zoo of hydrodynamic limits - some deterministic and some stochastic.

Solving Integer Programs (IPs) is generally NP-hard. But this does not imply that all instances are inherently hard. In fact, a substantial body of research has focused on identifying tractable subclasses and developing efficient (fixed-parameter tractable) time algorithms for those. This talk will give a little overview of some of the key results and techniques.

According to Sklar’s theorem, any multidimensional absolutely continuous distribution function can be uniquely represented as a copula, which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the conditional copula, especially when one does not have enough information to select the copula model. Several Bayesian methods to approximate the posterior distribution of functionals of the dependence varying according covariates are presented and compared; the main advantage of the investigated methods is that they use nonparametric models, avoiding the selection of the copula, which is usually a delicate aspect of copula modelling. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.

Given that all models are wrong, it is important to understand the performance of methods when the settings for which they have been designed are not met, and to modify them where possible so they are robust to these sorts of departures from the ideal. We present two examples with this broad goal in mind. \[ \] We first look at a classical case of model misspecification in (linear) mixed-effect models for grouped data. Existing approaches estimate linear model parameters through weighted least squares, with optimal weights (given by the inverse covariance of the response, conditional on the covariates) typically estimated by maximizing a (restricted) likelihood from random effects modelling or by using generalized estimating equations. We introduce a new ‘sandwich loss’ whose population minimizer coincides with the weights of these approaches when the parametric forms for the conditional covariance are well-specified, but can yield arbitrarily large improvements when they are not. \[ \] The starting point of our second vignette is the recognition that semiparametric efficient estimation can be hard to achieve in practice: estimators that are in theory efficient may require unattainable levels of accuracy for the estimation of complex nuisance functions. As a consequence, estimators deployed on real datasets are often chosen in a somewhat ad hoc fashion and may suffer high variance. We study this gap between theory and practice in the context of a broad collection of semiparametric regression models that includes the generalized partially linear model. We advocate using estimators that are robust in the sense that they enjoy root n consistent uniformly over a sufficiently rich class of distributions characterized by certain conditional expectations being estimable by user-chosen machine learning methods. We show that even asking for locally uniform estimation within such a class narrows down possible estimators to those parametrized by certain weight functions and develop a new random forest-based estimation scheme to estimate the optimal weights. We demonstrate the effectiveness of the resulting estimator in a variety of semiparametric settings on simulated and real-world data.