Bob Schacht <r_schacht@...> wrote:
Oh, I see. It's YOUR gold standard. Saying that something is the "gold
standard" usually means, to most people, that there is consensus agreement
about it. That is obviously not the case here.
Dave: As Bruce pointed out there are two camps. The Bayesian camp, would agree with me, and well, the other camp would disagree. Probably not much more to say there without going well outside the scope of the list. But for those with any interest at all - check out that power-point link from the earlier post, and if still interested the references at the end. There are some connections to the history of philosophy and religion that those in the humanities would find interesting. For example, Bayes may have written as a corrective to Hume. LaPlace is famous for the quote attributed to him of having no need for the "God hypothesis". Then Venn was a very conservative Christian. If you think about how loaded a word "belief" is in Christianity, and the fact that LaPalce claimed a mathematical formula for correct belief, you see there was more going on there than just a debate of technical merits. But then by the WWII era, the debate turns around. Now it is those associated with Skinner's behaviorism that like the frequency model, because Bayesian's talk of internal subjective probability seems to suggest that man is more than a machine. I don't think Bayesian is pro-religious or anti-religious, but the nature of the debate of the day may make its use more preferable to one side or the other.
>Yes, the correct Bayesian answer depends on your information set. Two
>different people with two different sets of information will get two
B: I think it is useful to focus on this point a bit, because this is
important in understanding Bayesian inference.
This answer demonstrates that Bayesian inference is not particularly useful
in establishing objective truth, unless there is consensus agreement on the
"information sets." Since it is manifestly clear that there is not much
agreement on the "information sets" with respect to the historical Jesus,
one can expect, at most, that Bayesian inference can help an individual
determine his/her own truth, but not in determining "the" truth.
D: In my case with "salt", I'm not looking for the historical Jesus, but the mind of the author "Mark". I'm trying to do a literary approach there. So, I would not be concerned with how probable it is Jesus walked on water, but only the probability that what Mark really wanted to communicate was that Jesus physically walked on water. And obviously setting probabilities to 0 or 100 based on faith would be out of bounds in a literary approach.
The information set is indeed key. I've already come to the conclusion that I need to be very explicit about what information set I'm relying upon. Then, unless I make errors, the only legitimate objection would be "But you didn't consider this piece of information".
B: The Jesus Seminar has done the same thing with
respect to the sayings and actions of Jesus: Anything coded red or pink is
"not junk," and anything coded black and grey is "junk" for purposes of
reconstructing the historical Jesus. The trouble is that those
classifications are the result of averaging the votes of many people, so
even the participants of the Jesus Seminar would not necessarily accept the
verdict for each item.
D: I think you're right. I think that does represent an attempt at sort of a "Bayesian group-think". The question of the historical Jesus, however, is probably much to broad to carefully define the relevant information sets, so the result it just the average of the individual subjective opinions. I'm now thinking that if I'm careful, however, I can come up with a good approximation of the relevant information sets for those 3 lines in Mark. And if I've omitted important information it should be obvious what was omitted, and then the reader would be able to mentally correct for the omission, offer brief, to the point, feedback, etc.
B: And I hardly think he is the "only" one in any useful
sense. Wouldn't that be a bit like claiming that only the writer of a spam
message would know whether or not it was spam?
D: I think you were thinking "historical" and I was thinking "literary approach to Mark". Mark is the only one that could possibly be 100% certain of what he was thinking.
Statistician / Sr. Systems Engineer
B.S. / M.S. Physics
M.S. Finance (ABD Management Science)
[Non-text portions of this message have been removed]