Blurb::
Discrete, epistemic uncertain variable - integers within a set
Description::
Discrete set variables may be used to specify categorical choices which are
epistemic. For example, if we have three possible forms for a physics
model (model 1, 2, or 3) and there is epistemic uncertainty about
which one is correct, a discrete uncertain set 
may be used to represent this type of uncertainty.

This variable is defined by a set of integers, in which the discrete value may
take any value within the integer set (for example, the set may be
defined as 1, 2, and 4)

Other epistemic types include:
\li \ref variables-continuous_interval_uncertain
\li \ref variables-discrete_interval_uncertain
\li discrete_uncertain_set \ref variables-discrete_uncertain_set-string
\li discrete_uncertain_set \ref variables-discrete_uncertain_set-real

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\li discrete_uncertain_set \ref variables-discrete_uncertain_set-integer

In addition to continuous and discrete aleatory probability
distributions, %Dakota provides support for continuous and discrete
epistemic uncertainties through the keywords:

Interval-based and set variables do not represent probability distributions.
-->

Topics::	discrete_variables, epistemic_uncertain_variables
Examples::
Let d1 be 2 or 13 and d2 be 4, 5 or 26.
The following specification is for an interval analysis:
\verbatim
discrete_uncertain_set
 integer
 num_set_values 2     3
 set_values     2 13  4 5 26
 descriptors    'di1' 'di2'
\endverbatim

Theory::
The \c discrete_uncertain_set-integer
variable is NOT a discrete random variable.
It can be contrasted to a the histogram-defined random variables:
\ref variables-histogram_bin_uncertain and \ref variables-histogram_point_uncertain.
It is used in epistemic uncertainty analysis, where one is trying to model 
uncertainty due to lack of knowledge. 

The discrete uncertain set integer variable is used in both interval analysis 
and in Dempster-Shafer theory of evidence.

\li interval analysis
-the values are integers, equally weighted
-the true value of the random variable is one of the integers in this set
-output is the minimum and maximum function value conditional
on the specified inputs

\li Dempster-Shafer theory of evidence
-the values are integers, but they can be assigned different weights
-outputs are called "belief" and "plausibility." 
Belief represents the smallest possible probability that is consistent with the evidence, 
while plausibility represents the largest possible probability that is consistent with the evidence. 
Evidence is the values together with their weights.

Faq::
See_Also::	
