Séance du 9 février 2015

Séance organisée par Marc Hoffmann et Pierre Latouche.

Lieu : IHP, Amphithéâtre Hermite.

14h00: Benjamin Holcblat (BI Norwegian Business School)

Titre : Econometric inference and multiple use of the same data .

Résumé : In fields that are mainly nonexperimental, such as economics and finance, it is unescapable to compute test statistics and confidence regions that are not probabilistically independent from previously examined data. We remind and formalize the inadequacy of the Bayesian and Neyman-Pearson inference theories for such a practice. Then, we present elements of a general econometric theory, called the neoclassical inference theory, that is immune to multiple use of the same data, modulo approximation error. The neoclassical inference theory appears to nest parameter calibration, and most econometric practices, whether they are labelled Bayesian or à la Neyman-Pearson.

15h00: Judith Rousseau (Cérémade, Université Paris-Dauphine)

Titre : Asymptotic properties of empirical Bayes procedures - From parametric to nonparametric models

Résumé : In this work we investigate frequentist properties of Empirical Bayes procedures. Empirical Bayes procedures are very much used in practice in more or less formalized ways as it is common practice to replace some hyperparameter in the prior by some data dependent quantity. There are typically two ways of constructing these data dependent quantities: using some kind of moment estimator or some quantity whose behaviour is well understood or using a maximum marginal likelihood estimator. In this work we .first give some general results on how to determine posterior concentration rates under the former setting , which we apply in particular to two types of Dirichlet process mixtures. We then shall discuss more parametric models in the context of maximum marginal likelihood estimation. We will in particular explain why some pathological behaviour can be expected in this case. We will .finally discuss some recent advances on maximum marginal likelihood empirical Bayes approaches in nonparametric setting.

16h00: Julien Chiquet (Laboratoire Statistique et Génôme, Université d'Evry Val d'Essonne)

Titre : Fast tree inference with weighted fusion penalties

Résumé : Given a data set with many features observed in a large number of conditions, it is desirable to fuse and aggregate conditions which are similar to ease the interpretation and extract the main characteristic of the data. This paper presents a multidimensional fusion penalty framework to address this question when the number of conditions is large. If the fusion penalty is encoded by a norm, we prove for uniform weights that the path of solutions is a tree which is suitable for interpretability. For the l1 and l∞ norms, the path is piecewise linear and we derive an homotopy algorithm to recover exactly the whole tree structure. For weighted l1-fusion penalties, we demonstrate that distance decreasing weights lead to balanced tree structures. For a subclass of these weights that we call “exponentially adaptive”, we derive an O(n log(n)) homotopy algorithm and we prove an asymptotic oracle property. This guarantees that we recover the underlying structure of the data efficiently both from a statistical and computational point of view. We provide a fast implementation of the homotopy algorithm for the single feature case, as well as an efficient embedded cross-validation procedure that takes advantage of the tree structure of the path of solutions. Our proposal outperforms its competitors on simulations both in term of timings and prediction accuracy. As an example we consider phenotypic data : given one or several traits, we reconstruct a balanced tree structure and assess its agreement with the known taxonomy.