I am under the impression that Bayesians believe in measurable parameters, such as physics, or counting up the sides of a die, in real world physical truths that they derive probabilities from… taken in the here and now as constants of the system. And frequentists look to long run behavior, historical documentation, expectation found through a series of attempts, empirically documented. A Bayesian will measure the weight of a die to determine if its balanced or if it favors one outcome, a frequentist will decide from observation.

Im just very confused about the various definitions of probability.

What if I said that the coin star question, the probability was 1/100… because there are only 100 possible distinct fractions of a dollar that we could arrive at. We can arrive at 0 cents surplus with the same likelihood of 99 cents or of 56 cents.

I would have called myself a Bayesian because I can count the possibilities up, and assuming they are all equally likely. If I ran the test many times to check, then Id be a frequentist. And yet subjectivists operate on a degree of confidence? Isnt that arbitrary? I could say that the probability is 50%… because that is how “confident” I feel.

The way I understand this, the result of the analysis would *not* assign a probability to the Bard’s authorship, but rather the probability that the association between the word frequencies found in the manuscript and those used by the Bard would be expected to occur by chance. The distinction is of no small matter, in my opinion, and at the root of many problems for scientists, who believe that a very small probability that the association between two things would be due to chance vindicates their chosen hypothesis, e.g., that Shakespeare probably wrote the play. While this line of thinking is important to rule out the role of chance, it does not by itself advance the positive assertion that Shakespeare wrote it by a micron. For example, we might take p < .0000001 as proof positive only to later find the manuscript was forged by a scholar in 1935. How silly we would look…

Respectfully,

Tom

At first I thought the subjectivist position was ridiculous: why be subjective when you can be objective? But then I realized that it’s not always possible to be objective. In that case you can either be explicit about your subjectivity, or keep it implicit and pretend it doesn’t exist.