Dakota Reference Manual  Version 6.4 Large-Scale Engineering Optimization and Uncertainty Analysis
integer

Discrete, epistemic uncertain variable - integers within a set

## Topics

This keyword is related to the topics:

## Specification

Alias: none

Argument(s): INTEGER

Default: no discrete uncertain set integer variables

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

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 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:

## Examples

Let d1 be 2 or 13 and d2 be 4, 5 or 26. The following specification is for an interval analysis:

```discrete_uncertain_set
integer
num_set_values 2     3
set_values     2 13  4 5 26
descriptors    'di1' 'di2'
```

## 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 conditional on 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.