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 discussed Quantum Bayesian theory here about three weeks ago. But now that I know what to look for, it has become easier to find more about it, so I come back to it. Early this year, the William & Mary blog ran an interview with Hans Christian von Baeyer, who believes that QB-ism (which he pronounces "cubism" as in Picasso) is nothing less than the "future of physics." He regrets that advocates of QBism have yet to get it into physics textbooks. But there are "hundreds of articles and conference proceedings" that deal with it, so he is hoping admission into the canon, with the dozen or so older interpretations of quantum mechanics, will come soon. Von Baeyer also makes reference to "an excellent article" that was added to the Stanford Encyclopedia of Philosophy in December 2016. So, after finishing up the interview, I went there. The actual title of that article is evidence that this is an appropriate thing to be discussing in a blo...
We discussed quantum theory yesterday. Now it is time to remind ourselves of the other half of our proposed mash-up. 'Bayesianism' is an approach to probability theory that begins with subjectivity, with somebody's guess about what is the likelihood of an event. It then discusses how an individual having certain circumstances may change his beliefs rationally, and (assuming he has beliefs on more than one question) may keep them consistent with one another -- or, in other words, how he may keep his view of the world coherent. The chief rival of Bayesianism is "frequentism." This treats probability as an objective fact in the world, another name for the frequency of some outcomes vis-a-vis others. I've discussed this difference before. But ... what does it have to do with quantum theory? Collapse the Function for your own Damned Self With a Bayesian approach we get a take on quantum theory that doesn't shrug its shoulders at the "what is rea...
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.
Okay, I think I have a fix on this. Suppose we want to test our hypothesis that otherwise comparable firms with high levels of indebtedness cut back on expenditures desired by employees in circumstances where their not-so-indebted cousins would not. (For a further explanation of that hypothesis, review Part I of this discussion from last week.) How do we do it? We'll assume that we haven't found a smoking gun memo in which the company's Treasurer writes to the CEO and says, "we can't afford those darn safety vests any longer. Tell Human Resources to stop buying them so we can make the interest payments!" Assume we're looking at circumstantial evidence. What counts as evidence? What we can't do is simply say: firm X buys safety vests for its employees and is mostly equity financed. Firm Y doesn't and isn't. No matter how many Xs and Ys we find compliant with our hypothesis, we will still have only correlation, not causation. The arrow of...
How can we use statistics to get at causal impact? Of course, correlation does not imply causation. Remember my lesson from a Dilbert's comic last week. But still, there are inferences to be drawn somehow. It may be a fact that MacDonald's just spent a lot of money on an ad campaign involving firecrackers and tapdancing penguins. It may be, also, that they sold a million hamburgers worldwide yesterday. It does not follow that they sold the million hamburgers because of that ad campaign. What MacDonald's clearly wants is some idea of how many hamburgers they would have sold if they had had some other ad campaign in place, possibly some less expensive campaign. Something involving their familiar clown and his sidekicks. Here's a social sciency thing about "Bayesian structural time-series models" that aims at getting at the problem. It's actually based on the experiences of Google, paid clicks versus free clicks, etc. -- I just prefer the MacDonald...
Some random reading again. Probability in the Philosophy of Religion. 2012. Much of the text is available on Google books . One big question in the P of R that involves probability in some sense is the evidence for miraculous events. Suppose a theist puts it forward as one of his reasons for belief in God that "only this belief can explain the parting of the Red Sea." One classic response, formulated for example by David Hume, is that the historical evidence for the event can never be greater than the improbability of the event. So it is always more rational to believe that the alleged miracle didn't happen, and the chain of testimony that has brought us news thereof is at fault, than to believe that it did happen, and qualify our belief in laws of nature in the process. This seems, then, squarely an argument about probability, and some of the contributions to this collection address it. One of the contributions that does is written by Benjamin C. Jantzen, of...