Talking about Probability, Inference and Decisions. Part 1: The Witches of Bayes

In October 2017 the Italian National Institute of Statistics (ISTAT), Italy's body for official statistics, has published the book of fairy tales Le streghe di Bayes (The witches of Bayes) written by ISTAT staff members with the commendable aim of introducing statistical and probabilistic reasoning to children. In this paper the fairy tale which gives the name to the book is analyzed in a dialog between three teachers with different background and expertise. The outcomes are definitively discouraging, especially when the story is compared to the appendix of the book, in which the teaching power of every story is indeed explained (as a matter of fact, without the appendix the fairy tale of the witches seemed to be written with the purpose of make the 'Bayesians', meant as the villagers from 'Bayes', ridiculous). In fact the fairy tale of the witches does not contain any Bayesian reasoning, the suggested decision strategy is simply wrong and the story does not even seem to be easily modifiable (besides the trivial correction of the decision strategy) in order to make it usable as a teaching tool. As it happens in real dialogues, besides the fairy tale in question, the dialogue touches several issues somehow related to the story and concerning probability, inference, prediction and decision making. The present paper is an indirect response to the invitation by the ISBA bulletin to comment on the fairy tale.
Comment: 48 pages, 14 figures, in Italian, be published in Progetto Alice, Rivista di matematica e didattica