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bayes-rules / bayesrules

📦 R package for Supplemental Materials for the Bayes Rules! Book
https://bayes-rules.github.io/bayesrules/docs/
GNU General Public License v3.0
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Misleading formulation of "variability" in the exercise 3.1b #87

Closed RaibekTussupbekov closed 2 years ago

RaibekTussupbekov commented 2 years ago

First of all, thank you very much for this titanic work you've done!

Exercise 3.1 (Tune your Beta prior: Take I) In each situation below, tune a Beta(α,β) model that accurately reflects the given prior information. In many cases, there’s no single “right” answer, but rather multiple “reasonable” answers. b. A scientist has created a new test for a rare disease. They expect that the test is accurate 80% of the time with a variance of 0.05.

I suspect that "a variance of 0.05" actually means "a variability of 0.05" that consequently is the standard deviation or SD(pi) but not Var(pi). I made this conclusion trying to simulate beta distribution in R with Var(pi) close to 0.05. That leads to beta extremely close to 1. On the other hand, with "a variance of 0.05" treated as SD(pi) I found reasonable values of alpha and beta, 48 and 12 respectively.

ajohns24 commented 2 years ago

Thanks for reading the book so carefully! "variance" not "variability" is the intended word here.