[Statlist] ETH Young Data Science Researcher Seminar Zurich - virtual seminar with Asaf Weinstein, Hebrew University of Jerusalem - Thursday, 10 November 2022

[Maurer Letizia]

We are glad to announce the following virtual talk in the ETH Young Data Science Researcher Seminar Zurich

"On permutation invariant problems in simultaneous statistical inference“  
by Asaf Weinstein, Hebrew University of Jerusalem

Date and Time: Thursday, 10 November 2022, 16:30-17:30 (Zurich time)
Place:  Zoom at https://ethz.zoom.us/j/68998616059

Abstract: Suppose you observe Y_i = mu_i + e_i, where e_i are i.i.d. from some fixed and known zero-mean distribution, and mu_i are fixed and unknown parameters. In this "canonical" setting, a simultaneous inference statistical problem, as we define it here, is such that no preference is given to any of the mu_i's before seeing the data. For example, estimating all mu_i's under sum-of-squares loss; or testing H_{0i}: mu_i=0 simultaneously for i=1,...,n while controlling FDR; or estimating mu_{i^*} where i^* = argmax{Y_i} under squared loss; or even testing the global null H_0 = \cap{i=1}^n H_{0i}. 

What is the optimal solution to a simultaneous inference problem? In a Bayesian setup, i.e., when mu_i are assumed random, the answer is conceptually straightforward. In the frequentist setup considered here, the answer is far less obvious, and various approaches exist for defining notions of frequentist optimality and for designing procedures that pursue them. In this work we define the optimal solution to a simultaneous inference problem to be the procedure that, for the true mu_i's, has the best performance among all procedures that are oblivious to the labels i=1,...,n. This is a natural and arguably the weakest condition one could possibly impose. For such procedures we observe that the problem can be cast as a Bayesian problem with respect to a particular prior, which immediately reveals an explicit form for the optimal solution. The argument actually holds more generally for any permutation-invariant model, e.g. when the e_i above are exchangeable, not independent, noise terms, which is sometimes a much more realistic assumption. Finally, we discuss the relation to Robbins's empirical Bayes approach, and explain why nonparametric empirical Bayes procedures should, at least when the e_i's are independent, asymptotically attain the optimal performance uniformly in the parameter value. 

Organisers: Alexander Henzi, Michael Law, Xinwei Shen


Seminar website: https://math.ethz.ch/sfs/news-and-events/young-data-science.html

Young Data Science Researcher Seminar Zurich – Seminar for Statistics | ETH Zurich
math.ethz.ch



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