"Kevin S. Van Horn" wrote:
> Can anyone tell me if belief-function theories such as Dempster-Shafer are
> capable of handling continuous domains? Shafer's book only discusses finite
> domains, and it's not at all obvious to me how one would generalize it to a
> continuous domain.
Yes. In fact the oft cited seldom read Dempster [1968] paper develops the
belief function generalization of the beta distribution.
The problem you are having is that if your domain is the real line between 0
and 1 (size aleph 1) then the domain of the measure function m() whould be of
size alph 2. The same thing happens in probability because P() is a set
function. You just pick a Borel set over the domain (i.e., the set of all
intervals plus their unions).
The useful belief functions tend to be random intervals whose endpoints have a
probability distribution of a known form. Dempster develops a "bivariate beta"
distribution in his paper. I develop a bivariate gamma in my book (Graphical
Belief Modeling).
--Russell Almond
This archive was generated by hypermail 2b29 : Sun Apr 02 2000 - 15:28:30 PDT