[extropy-chat] what is probability?
gts
gts_2000 at yahoo.com
Mon Jan 15 17:11:50 UTC 2007
On Mon, 15 Jan 2007 11:16:20 -0500, Russell Wallace
<russell.wallace at gmail.com> wrote:
> Seriously, that's why I said _practical_ example. If it matters, there
> should be real world cases that can serve as such. If it doesn't matter,
> well then it doesn't matter.
Not sure what you're getting at here, but assume you are political
pollster commissioned by a politician wanting to know the political
make-up of some newly districted congressional district about which there
is no reliable prior data, and at a time in which the entire country is in
political turmoil such that not even national statistics can be relied
upon for priors. Assume also that you don't care about third parties.
In that situation, if you are using bayesian methods, you might use the PI
and set your prior judgemental probability to .5 of finding, among those
voters in the district who say they belong to one of the two major
parties, someone who professes to be a democrat. You would then update
your judgemental probability as you condition on new evidence (new
interviews), just as in the urn example in which you would draw new
marbles, with the idea that your posterior judgemental probability will
converge in the limit with the objective chance of a person in that group
professing to be a democrat.
Now, as I indicated in my last message, our original prior above rests on
some shaky reasoning (the PI).
Opposing the PI is the idea that given no evidence, we should assign no
probability at all, i.e., that we should accumulate some empirical
evidence *before* we start estimating probabilities. But this idea makes
some bayesians very uncomfortable.
-gts
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