Dakota Reference Manual: discrete_interval_uncertain

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discrete_interval_uncertain

Epistemic uncertain variable - values from one or more discrete intervals

## Topics

This keyword is related to the topics:

- discrete_variables
- epistemic_uncertain_variables

## Specification

Alias: none

Argument(s): INTEGER

Default: No discrete interval uncertain variables

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Optional | num_intervals | Specify the number of intervals for each variable
| Optional | interval_probabilities | Assign probability mass to each interval
| Required | lower_bounds | Specify minimum values
| Required | upper_bounds | Specify maximium values
| Optional | initial_point | Initial values for variables
| Optional | descriptors | Labels for the variables

## 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:

- continuous_interval_uncertain
- discrete_uncertain_set integer
- discrete_uncertain_set string
- discrete_uncertain_set real

## 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:

    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

## Theory

- Dempster-Shafer theory of evidence -multiple intervals can be assigned to each `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.