Location Methods and Nash Equilibria for Experimental Design in Astrophysics and Aerospace Engineering

Daniele, Elia; Paolis, Pierluigi De; Greco, Gian Luca; D'Argenio, Alessandro

doi:10.1007/978-3-319-52654-6_4

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2020

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“…There are however some papers in the engineering literature cf. [9] and [7] dealing with design allocation problems which are addressed by finding the Nash equilibrium of a "design game". The game theoretic view provides a set of tools and method for reasoning in complex situations, which, we believe, will prove useful in solving variety of other problems in statistics.…”

Section: Summary and Discussionmentioning

confidence: 99%

On Bayes and Nash experimental designs for hypothesis testing problems

Singh¹,

Davidov²

2020

Electron. J. Statist.

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In this communication we examine the relationship between maxi-min, Bayes and Nash designs for some hypothesis testing problems. In particular we consider the problem of sample allocation in the standard analysis of variance framework and show that the maxi-min design is also a Bayes solution with respect to the least favourable prior, as well as a solution to a game theoretic problem, which we refer to as a Nash design. In addition, an extension to tests for order is provided. MSC2020 subject classifications: 62K05.

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Section: Summary and Discussionmentioning

confidence: 99%