.. _variables-discrete_uncertain_set-real:

""""
real
""""


Discrete, epistemic uncertain variable - real numbers within a set



**Topics**


discrete_variables, epistemic_uncertain_variables


.. toctree::
   :hidden:
   :maxdepth: 1

   variables-discrete_uncertain_set-real-elements_per_variable
   variables-discrete_uncertain_set-real-elements
   variables-discrete_uncertain_set-real-set_probabilities
   variables-discrete_uncertain_set-real-categorical
   variables-discrete_uncertain_set-real-initial_point
   variables-discrete_uncertain_set-real-descriptors


**Specification**

- *Alias:* None

- *Arguments:* INTEGER

- *Default:* no discrete uncertain set real variables


**Child Keywords:**

+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword            | Dakota Keyword Description                    |
|                         | Group              |                           |                                               |
+=========================+====================+===========================+===============================================+
| Optional                                     | `elements_per_variable`__ | Number of admissible elements for each set    |
|                                              |                           | variable                                      |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Required                                     | `elements`__              | The permissible values for each discrete      |
|                                              |                           | variable                                      |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `set_probabilities`__     | This keyword defines the probabilities for    |
|                                              |                           | the various elements of discrete sets.        |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `categorical`__           | Whether the set-valued variables are          |
|                                              |                           | categorical or relaxable                      |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `initial_point`__         | Initial values for variables                  |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `descriptors`__           | Labels for the variables                      |
+----------------------------------------------+---------------------------+-----------------------------------------------+

.. __: variables-discrete_uncertain_set-real-elements_per_variable.html
__ variables-discrete_uncertain_set-real-elements.html
__ variables-discrete_uncertain_set-real-set_probabilities.html
__ variables-discrete_uncertain_set-real-categorical.html
__ variables-discrete_uncertain_set-real-initial_point.html
__ variables-discrete_uncertain_set-real-descriptors.html



**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 reals, in
which the discrete variable may take any value defined within the real
set (for example, a parameter may have two allowable real values,
3.285 or 4.79).

Other epistemic types include:

- :dakkw:`variables-continuous_interval_uncertain`
- :dakkw:`variables-discrete_interval_uncertain`
- discrete_uncertain_set :dakkw:`variables-discrete_uncertain_set-integer`
- discrete_uncertain_set :dakkw:`variables-discrete_uncertain_set-string`




**Examples**



Let `dr1` be 2.1 or 1.3 and `dr2` be 0.4, 5 or 2.6.
The following specification is for an interval analysis:

.. code-block::

    discrete_uncertain_set
     integer
     num_set_values  2           3
     set_values      2.1  1.3    0.4  5  2.6
     descriptors     'dr1'       'dr2'





**Theory**


The ``discrete_uncertain_set-integer``
variable is NOT a discrete random variable.
It can be contrasted to a the histogram-defined random variables:
:dakkw:`variables-histogram_bin_uncertain` and :dakkw:`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.


*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 conditionalon the specified inputs


*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.