# Séminaire ICI : Michael Bell

## Titre du séminaire et orateur

On Universality and Training in Binary Hypothesis Testing.

Michael Bell (Hebrew University of Jerusalem)

## Date et lieu

Lundi 4 novembre 2019, 11h.

Salle 384, ENSEA

## Abstract

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified.

For the simple Gaussian location model, we overcome the difficulty as follows. In this problem there exists a natural “hardness” order between parameters, as the optimal error-probability curves of different parameters (when the

parameter is known) do not intersect. We can thus define the universal minimax performance as the worst-case among parameters which are at least equally hard. This criterion extend to the wide class of local asymptotic normal models, in an asymptotic sense where the approximation of the error probabilities is additive. As in the regime of interest the error probabilities do not vanish, the candidate distributions must “grow closer” as a function of blocklength, thus the question becomes that of “resolution”. Under this criterion we find the asymptotically optimal tests for composite hypothesis testing with and without training data, thus quantifying the loss of universality and gain of training data.

## Bio

Michael Bell is a statistician and a PhD student at the School fo Computer Science and Engineering, the Hebrew University of Jerusalem.