STAT 330 August 30, 2012

Today we finished an informal justification of the axioms of probability from the point of view of betting consistency. If you are going to make bets, you should not be able to be put into a condition where you will be guaranteed to lose the bets, regardless of the outcome. This puts you into a situation of inconsistency, or incoherence.

We then started looking at some very simple examples of joint, marginal, and conditional distributions. I noted that you cannot marginalize on stuff to the right of the conditioning bar ‘|’, the conditions. You can only marginalize (sum over) stuff to the left of the conditioning bar. But marginalization is an important part of Bayesian statistics. It is the way that we consider the things that we think are important.

I mentioned the astronomer Cecelia Payne, who discovered that stars were made mostly of hydrogen, even though their spectra seemed to indicate that they might have large amounts of other elements. She was a pioneering woman scientist, the first woman to hold a full professorship in Harvard’s Faculty of Arts and Sciences (after having been in low-paying and/or non-prestigious positions for a large part of her career, despite her enormous contributions to astronomy).

4 Responses to “STAT 330 August 30, 2012”

  1. Ahmed Says:

    Thank you, Professor Jefferys for going over this very elementary yet challenging material to understand!

    I found the justification of probability axioms to be counter-intuitive after we were taught in early age that the final outcome of an event and its compliment is always equal to 1. Having do the mind-bending, and pretend that they don’t add up to 1 was essentially challenging. Now, after the lecture explanation and notes, things are settling in. Thank you very much once again! Looking forward to the next class.

  2. Cathy Says:

    Actually, I had a question about that. In slide 36 of the “Introduction to Bayesian…”, I’m wondering why, on the first line, we have -(1-P(C|H)). It seems like it should be +(1-P(C|H)) because we’re talking about C being true on this line.

    • bayesrules Says:

      Good question, Cathy. The reason for the change in sign is you are betting in favor of A and B (separately), and against C=AvB. On Slide 35 it says that your opponent will be “forcing You to take one side of simultaneous bets on A and B, and the other side of a third simultaneous bet on C (all at the same stake c)” He does this by assigning +c to the bets on A and B and -c to the bet on C.

  3. Cathy Says:

    Great! Thank you – this helps to clarify 🙂

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