This youtube video is well done. https://www.youtube.com/watch?v=R13BD8qKeTg It's an explanation, through the hook of epidemiology and an unspecified dread disease, of the significance of Bayes theorem in probability. I'll leave you to watch it without any further gloss from me, except to mention that the theorem in question helped launch not just a new branch of probability theory, but a new and still controversial understanding of how all of probability theory ought to be understood. The other side in the Big Picture debate, the frequentists, accept the Theorem but take care to distinguish it from Bayesian philosophy. The photo above is of John Venn, of the famous Venn diagrams, the Big Cheese on the frequentist side of the debate.
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I have written before in this blog about the 'Bayesian' interpretation of probability. I have even discussed a construction of quantum mechanics that draws on Bayesianism. What I'd like to add today is a little bit of history. Bayesianism doesn't come from the Reverend Thomas Bayes. No more than Christianity comes from Jesus. No one seems to have thought Bayes' 18th century contributions to probability theory (real though they were) had a lot of philosophical weight until the early 20th century. It was Frank Ramsey who made that leap, who served as the Apostle Paul of our analogy. In the mid 1920s and through the early 1930s, Ramsey worked to axiomize a Bayesian/subjectivist approach to probability. [Ramsey is a relevant figure in the history of epistemology as well: he pioneered the minimalist account of truth.] H wrote, "[w]e have the authority both of ordinary language and of many great thinkers for discussing under the heading of probability what ap...
I'm torn on the value of Bayesianism in the philosophy-of-science context. I won't discuss my own conflicted position, but I will say that Michael Strevens covers the field pretty well in this article: http://www.strevens.org/research/simplexuality/Bayes.pdf There are, on Strevens' telling, three big points: 1) that a scientist's "epistemic attitude to any scientifically significant proposition is, or ought to be, exhausted by the subjective probability the scientist assigns to the proposition;" 2) that this subjective probability conforms to the standard mathematics of probability; and 3) that Bayes' conditionalization rule is an instruction as to how one ought to update one' subjective probabilities as new evidence arises. And, by the way, yes the "r" does appear where I've put it in Strevens' name. That isn't a typo.
P(H/D) = [P(D/H) x P(H)] ÷ P(D). That is one common formulation of Bayes' theorem, and at the heart of the view of statistics associated with a mid-18th century Englishman, Thomas Bayes. I blogged about this in January. If you don't understand the notation above, and would like a primer, go here. I bring it up again because Bayesianism has attracted new attention in the blogosphere. Sometimes the above is called "Bayes' rule," because it suggests a rule for constantly updating your views of the likelihood of events. Your hypothesis of probability of H on Tuesday (the prior ) is to be updated according to what happens or doesn't happen Wednesday, thereby yielding the posterior probability. Econoblogger Noah Smith wrote a post he calls " Bayesian Superman." He combines a (male)...
P(H/D) = [P(D/H) x P(H)] ÷ P(L) Thomas Bayes, a mid-eighteenth century English mathematician, dead since 1761, performed magic the ramifications of which continue to unfold, and in directions of interest to the world of finance today. But I won't really get into the applications here. I'll just state the main point associated wit...