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).
BayesRules 