Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Epistemic uncertain variable  values from one or more continuous intervals
This keyword is related to the topics:
Alias: interval_uncertain
Argument(s): INTEGER
Default: no continuous 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 
Continuous 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. All values between the bounds are permissible. 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:
The following specification is for an interval analysis:
continuous_interval_uncertain = 2 lower_bounds = 2.0 4.0 upper_bounds = 2.5 5.0
The following specification is for a DempsterShafer analysis:
continuous_interval_uncertain = 2 num_intervals = 3 2 interval_probs = 0.25 0.5 0.25 0.4 0.6 lower_bounds = 2.0 4.0 4.5 1.0 3.0 upper_bounds = 2.5 5.0 6.0 5.0 5.0
Here there are 2 interval uncertain variables. The first one is defined by three intervals, and the second by two intervals. The three intervals for the first variable have basic probability assignments of 0.2, 0.5, and 0.3, respectively, while the basic probability assignments for the two intervals for the second variable are 0.4 and 0.6. The basic probability assignments for each interval variable must sum to one. The interval bounds for the first variable are [2, 2.5], [4, 5], and [4.5, 6], and the interval bounds for the second variable are [1.0, 5.0] and [3.0, 5.0]. Note that the intervals can be overlapping or disjoint. The BPA for the first variable indicates that it is twice as likely that the value occurs on the interval [4,5] than either [2,2.5] or [4.5,6].
The continuous interval uncertain variable is NOT a probability distribution. Although it may seem similar to a histogram, the interpretation of this uncertain variable is different. It is used in epistemic uncertainty analysis, where one is trying to model uncertainty due to lack of knowledge. The continuous interval uncertain variable is used in both interval analysis and in DempsterShafer theory of evidence.
continuous_interval_uncertain
variable the interval is defined by lower and upper bounds the value of the random variable lies somewhere in this interval output is the minimum and maximum function value conditional on the specified intervalcontinuous_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.