The place I would start on both grounds in my Book (Almond [1995],
Graphical Belief Models, Chapman and Hall). The last (and largest)
third of the book is one extended example that looks at graphical
belief function for predicting system reliability.
A faster read from a purely theoretical perspective is a small white
paper I wrote on the subject as part of the graphical belief project.
It is on-line at:
http://www.stat.washington.edu/bayes/almond/pubs/valve.ps.Z
This give some simple examples in each of the frameworks showing the
advantages and complexit of each.
Another good starting point is:
{Shafer, G. [1990]} ``Perspectives on the Theory and
Practice of Belief Fucntions.'' {\it International Journal of
Approximate Reasoning,\/} {\bf 4}, 323--362.
The short version of my findings is that the intervals I generated
with the belief function model were slightly wider than those I got
with the "Bayesian" method (actually a Bayesian interpretation of a
frequentest method) for the same problem. However, as a caveat, my
model was based on the Fiducial belief functions (like Dempter
[1966,1968]). Philipe Smets and others have been working on different
generation models, which may have different properties. (Shafer
[1982] goes over the difference.)
{Shafer, G. [1982]} ``Belief Functions and Parametric
Models.'' {\it Journal of the Royal Statistical Society, Series B,\/}
{\bf 44}, 322-352.
As far as some of the other volumes which have been mentioned.
1) Although I do like Pearl's characterization of belief functions as
a "Probability of Provability", I don't like the example he chooses in
his book. For me, that problem is plagued with issues of using
uniform priors as non-informative. It is a difficult problem to sort
out from either the probability or belief function perspective.
Therefore, I don't find it particularly helpful.
2) Walley's book is very dense. I found it tough going, although
interesting. Some of Walleys criticisms of belief functions are spot
on. (I summarize some of them in my book.) If you are interested in
comparing belief functions to robust Bayes approaches, this is still
probably the best source.
I hope that gets you started.
--Russell Almond
Educational Testing Service
Research Statistics Group, 15-T
Princeton, NJ 08541
Phone: 609-734-1557 FAX: 609-734-5420
Email: --almond@acm.org, --ralmond@ets.org
http://www.stat.washington.edu/bayes/almond/almond.html
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