Class 13: No "Fair" Dice & Jaynes Symmetry

Lesson 13: No "Fair" Dice & Jaynes Symmetry
Uncertainty & Probability Theory: The Logic of Science

We learn that adding "fair" to the evidence of a die toss gives a circular argument: it assumes what it sets out to prove, that the probability is symmetric. We examine Jaynes's attempt to provide a proof of equi-probability, but we see that fails because of the same circularity. So does a proof by Diaconis, which you can read on the blog. Next time we do Stove's proof - which works!

Homework: We did Pr(M_6|E) = 1/6, and we did Pr(M_6|E + "fair") = 1/6 (a circular argument!). Now give us Pr(M_6|E + "unfair") = ?

The Infamous Coin Flipping Machine!
https://youtu.be/8XX0iRAN--8

All questions will be answered in the following Monday's lecture.

Written lecture: https://www.wmbriggs.com/post/51979/
https://wmbriggs.substack.com/

Permanent class page: https://www.wmbriggs.com/class/