Not being Postscript-enabled, and somewhat mathematically challenged
(both informational AND computational limitations on my part (-:), I'd
like to try and understand this a bit better (in English, if
possible).
<Consider two agents who want to be Bayesians with a common prior, but
who can not due to computational limitations.>
I suspect this should actually read "a [set of] common prior
[probabilities]". Or, perhaps, we are failing to communicate due to
informational limitations (unfamiliarity with terminology on my
part)?
It seems to me that your discussion must be limited to two experts who
can agree on the context of the problem being addressed. An expert
and a non-expert would not share the common background information
that would make application to the discussion of additional evidence
practical with Bayesian techniques.
<If these agents agree that they can reason abstractly about the fact
that they have these limitations, then they can only agree to disagree
about their estimate of a random variable if they agree to disagree
(to a similar degree) about both their average biases.>
Are these computational limitations you speak of the situation where
one party may not have the time or temperament to perform a complete
or correct inductive analysis?
Or, is one party simply unfamiliar with the formal analysis approach
and unable to *formulate* the necessary computation?
If the latter, isn't this, rather, an informational limitation?
On the one hand, with your emphasis on computational limitations, I
get the feeling that you're agreeing with many of the posters on this
thread that "common-sense" reasoning would be a different
computational approach from Bayesian analysis, even if the two parties
both had the same prior "information".
LDC 970325:
<I will also admit that it is quite possible that the number of
decisions I make using conscious reasoning is numerically overwhelmed
by those I make sub-consciously by simply following whatever memes
happen to floating in the soup.>
Curt Adams 970326:
<The obvious conclusion is that most if not all people do not use even
a passable approximation of Bayesian inference. I'd say most if not
all people have their opinions driven by memetic replication (as
exemplified by fashion and religion) and not a passable Bayesian
approximation.>
And, more recently on another thread, Steve Witham put it this way:
<you'll be lead into finding that the value (in hypothesized beings)
that is identical to what you (the analyzer) call success, will be the
one with the most stability, and everything else might as well be
coded (in your analysis) as ideas of how to achieve it.>
So, on the other hand, are you trying to show, vis a vis what Curt
said, that normal "memetic replication" actually *does* end up
equating to "a passable approximation of Bayesian inference"?
On 970326 you wrote to Lee (regarding his argument that using
inference to judge whether inference works best is a circular
argument):
<Come now, your behavior here seems a good example of the error of
refusing to give any weight to the opinions of others, unless they
present to you, at your convenience and in a form you can quickly
understand, all the evidence behind their opinions.>
It seems to me, as well, that sensible people will accept expert
opinions on some complex subject *only if* it can be presented in a
context they can understand. Isn't this a problem of using the
appropriate level of communication (information) rather than a
different type of computation (reasoning)?
It's not that I (or the average person) want(s) to ignore expert
opinions, it is simply that we can not make any use of them if they
can not put into terms we can understand. This is why I would tend to
say that, *in general*, disagreement is a matter of informational
rather than (or as well as) computational limitations.
Mark Crosby
P.S. For those who might be interested, there is a descent overview
called "A Short Exposition on Bayesian Inference and Probability" by
John Stutz & Peter Cheeseman at
http://ic-www.arc.nasa.gov/ic/projects/bayes-group/group/html/bayes-the
orem-long.html