In mathematics, a credal set is a set of probability distributions[1] or, more generally, a set of (possibly only finitely additive) probability measures.
It is intended to express uncertainty or doubt about the probability model that should be used, or to convey the beliefs of a Bayesian agent about the possible states of the world.
is closed and convex, then, by the Krein–Milman theorem, it can be equivalently described by its extreme points
In that case, the expectation for a function
with respect to the credal set
forms a closed interval
denotes a probability measure, and with a similar expression for
is a categorical variable, then the credal set
can be considered as a set of probability mass functions over
is also closed and convex, then the lower prevision of a function
denotes a probability mass function.
It is easy to see that a credal set over a Boolean variable
cannot have more than two extreme points (because the only closed convex sets in
are closed intervals), while credal sets over variables
that can take three or more values can have any arbitrary number of extreme points.
[citation needed] This probability-related article is a stub.