We use the theory of convex sets of probability distributions, referred to as Quasi-Bayesian theory [Giron & Rios1980]. Motivation for the use of this theory in inferences, and a summary of the theory, is available in a companion technical report [Cozman1996]. Here we outline the chief ideas behind Quasi-Bayesian theory.

Imprecision in probability assessments can be due either
to difficulties in eliciting information from experts,
or to difficulties in processing or combining data [Walley1991].
This imprecision is modeled by convex sets of distributions,
called *credal sets*. To simplify terminology, we use the term credal
set only when it refers to a set of distributions containing more than one
element. Convex sets of conditional distributions are used to represent
conditional beliefs. Inference is performed by applying Bayes rule to
each distribution in a prior credal set; the posterior credal set
is the union of all posterior distributions. An
introduction to technical aspects of Quasi-Bayesian theory,
with a larger list of references, can be found at
http://www.cs.cmu.edu/~fgcozman/qBayes.html.

Given a Quasi-Bayesian credal set K, a probability interval is induced for every event A:

__p__(A) = _{p is in K} p(A)

~~p~~(A) = _{p is in K} p(A).

Lower and upper expectations for a function u() are defined as:

__E__[x_{q}] = _{p} E_{p}[u]

~~E~~[x_{q}] = _{p} E_{p}[u],

© Fabio Cozman[Send Mail?]

Thu Jan 23 15:54:13 EST 1997