Re: Bayesian Networks and Belief Functions
WANG Pei (pwang@cogsci.indiana.edu)
Mon, 7 Jun 1999 06:23:12 -0500 (EST)
> From: David Poole <poole@cs.ubc.ca>
>
> Rolf Haenni wrote:
> > But knowing that P(Q)=0.5 is
> > clearly not the same as to know nothing about Q.
>
> This isn't so clear. Here is some reasoning I have used to convince
> myself that these are indeed the same:
>
> Suppose we have a button, and when we press the button, there is one of
> two outcomes, either a H or a T (just to make it look familiar). Let the
> event Q be the outcome of pressing the button.
>
> Before we press any buttons, I ask you what will be the first outcome.
> You, of course, say "I don't know".
>
> Suppose we press the button 4 times and observe a H,T,T,H. And then I
> ask you what will be the outcome of the 5th press. You then would also
> say "I don't know".
>
> Now suppose that we were to press the button 1,000,000 times and we
> observe that half of them resulted in H and half resulted in T (and we
> could not detect a pattern in the sequence). If I then ask you to say
> what the outcome of the 1,000,001st press will be, you would also say "I
> don't know".
Yes, as long as current belief is concerned, the above three
situations (0:0, 2:2, and 500000:500000) are the same: "I don't know
(whether the next outcome will be H or T)."
However, what distinguishes ignorance and known probability is how new
evidence will revise current belief. After a new H (or T) is
observed, the above three cases become different. I'd like to know
how this difference can be captured by BN.
Pei
http://www.cogsci.indiana.edu/farg/pwang.html