Re: Probability-Possibility Consistency

WSiler (wsiler@aol.com)
Mon, 8 Dec 1997 02:08:55 +0100 (MET)

On Fri, Nov 28, Ellen Hisdal wrote:

>Prob(ui)=P(ui|a)=probability that an object which has been labeled yes-a
>by a subject has the (exactly measured) height ui.
>
>Poss(ui)=Prob(a|ui)=probability that a subject will assign to an object of
>(exactly measured) height ui the label yes-a.
>
>
I have no problem with the definition of Poss(ui)l. However, I do have a
problem with the definition of Prob(ui). Here we are into probability with a
continuous argument. Ordinarily, this would be described by a probability
density function on ui, with the usual restriction of area = 1. The probability
that any one exactly measured ui would have produced the label would be zero:
the density function would be, of course, d(cumprob(ui|a)/dui. I think we could
talk about the likelihood that a height labeled yes-a would have exactly the
value ui, but that is a different story, and such a likelihood could range from
zero to a maximum of infinity for a crisp number.

Am I missing something?