Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Epistemic uncertain variable  values from one or more discrete intervals
This keyword is related to the topics:
Alias: discrete_uncertain_range
Argument(s): INTEGER
Default: No discrete interval uncertain variables
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  
Optional  descriptors  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. 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 DempsterShafer 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 DempsterShafer 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
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.