Class 29: Nothing Has A Distribution

Lesson 29: Nothing Has A Distribution

DO TO CIRCUMSTANCES, I'VE HAD TO CHANGE THE SETTING FOR A WEEK OR TWO.

But I made a mistake in the book and didn't correct in the video! I correct it here.

We'll talk about this many times. Here it is simple. Suppose Sally takes a college class that is graded on a scale 0, 1, 2, 3, 4, and no other numbers are possible. She takes one class. We deduce her GPA could be, and only could be, 0, 1, 2, 3, 4. There are no other possibilities.

Now suppose she takes two classes. The GPA possibilities are now 0, 0.5, 2, 2.5, ..., 4. There are no other possibilities. The mistake in Uncertainty is assuming each of these is equally likely. They are not, given G. Given G' = "The possibilities are 0, 0.5, 2, 2.5, ..., 4", which is not G, the probabilities of each GPA are equal. Given G, they are not. Because, for instance, there are two ways to get 0.5, a fact we deduce from G, but not G'. If you read the book substituting G' in for G, all works. Homework is to figure right correct probabilities.

Since nothing has a probability, and probability does not exist, nothing can have a distribution, either. There are no "means", "standard deviations" and the like, as "true" values: these words are anyway equivocal. It turns out probabilities are models!

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

Written lecture:
https://www.wmbriggs.com/post/53989/
https://wmbriggs.substack.com/p/151636120

Jaynes's book (first part): https://bayes.wustl.edu/etj/prob/book.pdf

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

Uncertainty & Probability Theory: The Logic of Science