Blurb::
Epistemic uncertain variable - values from one or more discrete intervals

Description::
Discrete interval uncertain variables are epistemic types.  They can
specify a single interval per variable which may be used in interval
analysis, where the goal is to determine the interval bounds on the
output corresponding to the interval bounds on the input. Permissible
values are any integer within the bound.  More detailed continuous
interval representations can specify a set of belief structures based
on intervals that may be contiguous, overlapping, or disjoint. This is
used in specifying the inputs necessary for an epistemic uncertainty
analysis using Dempster-Shafer theory of evidence.

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

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, 3 or 4 with probability 0.2, 4 or 5 with probability 0.5 and 6 with probability 0.3. 
Let d2 be 4, 5 or 6 with probability 0.4 and 6, 7 or 8 with probability 0.6.
The following specification is for a Dempster-Shafer analysis:
\verbatim
discrete_interval_uncertain = 2
 num_intervals = 3 2
 interval_probs = 0.2 0.5 0.3 0.4 0.6
 lower_bounds = 2 4 6 4 6
 upper_bounds = 4 5 6 6 8
\endverbatim

Theory::
\li Dempster-Shafer theory of evidence
-multiple intervals can be assigned to each \c discrete_interval_uncertain variable
-a Basic Probability Assignment (BPA) is associated with each interval. The BPA represents a probability that the value of the uncertain variable is located within that interval. 
-each interval is defined by lower and upper bounds
-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 intervals together with their BPA.

Faq::
See_Also::	
