real

Discrete, epistemic uncertain variable - real numbers within a set

Topics

discrete_variables, epistemic_uncertain_variables

Specification

• Alias: None

• Arguments: INTEGER

• Default: no discrete uncertain set real variables

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
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

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:

• continuous_interval_uncertain

• discrete_interval_uncertain

• discrete_uncertain_set integer

• 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:

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: histogram_bin_uncertain and 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.