Teaching Decision Theory Proof Strategies Using a Crowdsourcing Problem

Content Provider	Scilit
Author	Esteves, Luís Gustavo Izbicki, Rafael Stern, Rafael Bassi
Copyright Year	2017
Description	Journal: The American Statistician Teaching how to derive minimax decision rules can be challenging because of the lack of examples that are simple enough to be used in the classroom. Motivated by this challenge, we provide a new example that illustrates the use of standard techniques in the derivation of optimal decision rules under the Bayes and minimax approaches. We discuss how to predict the value of an unknown quantity, θ ∈ {0, 1}, given the opinions of n experts. An important example of such crowdsourcing problem occurs in modern cosmology, where θ indicates whether a given galaxy is merging or not, and $Y_{1}$, …, $Y_{n}$ are the opinions from n astronomers regarding θ. We use the obtained prediction rules to discuss advantages and disadvantages of the Bayes and minimax approaches to decision theory. The material presented here is intended to be taught to first-year graduate students.
Related Links	http://arxiv.org/pdf/1905.07670
Ending Page	343
Page Count	8
Starting Page	336
ISSN	00031305
e-ISSN	15372731
DOI	10.1080/00031305.2016.1264316
Journal	The American Statistician
Issue Number	4
Volume Number	71
Language	English
Publisher	Informa UK Limited
Publisher Date	2017-10-02
Access Restriction	Open
Subject Keyword	Journal: The American Statistician Bayes Decision Crowdsourcing Problem Minimax Decision
Content Type	Text
Subject	Statistics and Probability Statistics, Probability and Uncertainty