Actually, I think we agree on physical verses subjective probabilities. I
was just not being careful in my terminology (calling a relative frequency
a probability).
I was trying to be funny about `manipulating' x-squared into x-cubed. I
could be just as facetious about manipulating true variables: `A variable
is a symbol that represents any member of some set. So to manipulate that
symbol must be to turn say x into y.'
However, seriously it is much easier to formally define manipulating a
variable than a function:
-We say we `manipulate' variable X when, by a means external to the system
being modeled, we force X to a particular value.
-We say we `manipulate' function X when, by a means external to the system
being modeled, we force the arguments of X to particular values.
This is my real problem with X being a function. To be precise we have to
keep saying things in a difficult, unintuitive way. Again (and I keep
saying this) I do not want to change the definition of a random variable. I
am arguing not to use random variables in most applications of Bayes' rule.
Just use a plain old variable.
Sincerely,
Rich
At 04:16 PM 6/24/98 -0500, Kevin Korb wrote:
>Re manipulating functions... Rich wrote:
>
>> But, like I said, you are manipulating the input to control the value
>> returned by the function; you are not manipulating the function.
>
>But that's what we mean by "manipulating the function." Since the
>whole discussion seems to be about settling upon a common set
>of conventions about how to use words, it seems to me that my
>invocation of ordinary language meaning is pertinent.
>
>> The only
>> way to manipuluate a function (say x-squared) is to turn it into say
>> x-cubed. Remember a function, by definition, is a set of ordered pairs.
>
>That's problematic. How can you be manipulating "a" function here?
>It seems to me that x^2 and x^3 are two functions rather than one.
>So this appears not to be a possible way of talking about manipulating
>functions.
>
>As for my terminological preference for "random variable" or "uncertain
>quantity" talk, I prefer consistency with Savage's usage (i.e., RV),
>since I fail to see a reason to change. Although I'm no reactionary,
>I'm prepared to let the dead hand of convention win, when there's
>no positive reason to change.
>
>About physical vs. subjective probabilities I again differ...
>
>> 1) In a Bayesian application we manipulate probabilities. If we claim they
>> are physical (relative frequencies), then we need to include our confidence
>> in them and compute our confidence in the inferred probabilities (it is not
>> same).
>
>First, relative frequencies aren't probabilities at all, even if
>they provide evidence for probabilities. Physical probabilities are
>a distinct kind of beast. I believe the best treatment of the
>relation between physical and subjective probability is that
>of David Lewis -- "A Subjectivist's Guide to Objective Chance,"
>in R. Jeffrey (1980) Studies in Inductive Logic & Probability, II.
>I'd be interested in your response to that.
>
>There is, of course, the need to have subjective probabilities about
>our objective probabilities, just as we need (as inductive
>agents) to have subjective probabilities about any of our theories
>about the physical world.
>
>> 2) Even if (1) is overcome, we now have a problem when the probability is
>> clearly not physical....
>
>I can't see how there's a problem here; but then I'm hardly
>a frequentist, even if I fail to live up to born-again expectations.
>
>> I really do not want to discuss physical verses subjective probabilities
>> anymore. I have had that discussion 1000 times.
>
>I think there's plenty to be said in this general area that hasn't
>yet been said. I'm working on a paper (partially) on the subject, in fact.
>
>Cheers, Kevin
>
>