The standard derivation of the formula 3-18 in the PDF version is to create a sample space of all ways to draw n balls, count the number of ways to draw r red balls and n-r non-red balls, and divide the latter by the former, claiming each is equally likely.
Jaynes invokes identical combinatorics, but changes his language to speak of mutually-exclusive propositions and the principal of indifference instead of measuring a space.
How much of frequentist probability can be transformed into Bayesian by a simple change in language? Can this be formalized into a proof that they achieve the same results where applicable?
Isn't the equivalence of the "superstructure" implicit in that both systems satisfy (and can be derived from) the Kolmogorov axioms (Section 2.6.4 of the book)?
Of course Jaynes claims in 2.6.4 that his version of Bayesianism goes beyond Kolmogorov (I'm guessing he is talking about things like the principle of indifference and MAXENT.)
Previously: Book Club introductory post - Chapter 1 - Chapter 2
We will shortly move on to Chapter 3 (I have to post this today owing to vacation - see below). I have updated the previous post with a summary of chapter 2, with links to the discussion as appropriate. But first, a few announcements.
How to participate
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If you are still participating, please let the group know - all you have to do is fill in the "Active (Chapter)" column. Write in an "X" if you are checked out, or the number of the chapter you are currently reading. This will let us measure attrition, as well as adapt the pace if necessary. If you would like to join, please add yourself to the spreadsheet. If you would like to participate in live chat about the material, please indicate your time zone and preferred meeting time. As always, your feedback on the process itself is more than welcome.
Refer to the Chapter 1 post for more details on how to participate and meeting schedules.
Facilitator wanted
I'm taking off on vacation today until the end of the month. I'd appreciate if someone wanted to step into the facilitator's shoes, as I will not be able to perform these duties in a timely manner for at least the next two weeks.
Chapter 3: Elementary Sampling Theory
Having derived the sum and product rules, Jaynes starts us in on a mainstay of probability theory, urn problems.
Readings for the week of 19/07: Sampling Without Replacement - Logic versus Propensity. Exercises: 3.1
Discussion starts here.