discrete_interval_uncertain

Epistemic uncertain variable - values from one or more discrete intervals

Topics

discrete_variables, epistemic_uncertain_variables

Specification

• Alias: None

• Arguments: 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, e.g., [1, 4], allowing discrete values of 1, 2, 3, or 4)

Discrete variables may be used to represent things like epistemic model form uncertainty. For example, if one wants to analyze the effect of model 1 vs. model 2 vs. model 3 in an epistemic analysis (either an interval analysis or a Dempster-Shafer evidence theory analysis), one can use a discrete epistemic variable to represent the uncertainty in the model form.

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

• integer

• string

• 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.