Epistemic uncertain variable - values from one or more discrete intervals


discrete_variables, epistemic_uncertain_variables


  • Alias: None

  • Arguments: INTEGER

  • Default: No discrete interval uncertain variables

Child Keywords:


Description of Group

Dakota Keyword

Dakota Keyword Description



Specify the number of intervals for each variable



Assign probability mass to each interval



Specify minimum values



Specify maximium values



Initial values for variables



Labels for the variables


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:


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


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.