1Blurb:: 2Discrete, epistemic uncertain variable - integers within a set 3Description:: 4Discrete set variables may be used to specify categorical choices which are 5epistemic. For example, if we have three possible forms for a physics 6model (model 1, 2, or 3) and there is epistemic uncertainty about 7which one is correct, a discrete uncertain set 8may be used to represent this type of uncertainty. 9 10This variable is defined by a set of integers, in which the discrete value may 11take any value within the integer set (for example, the set may be 12defined as 1, 2, and 4) 13 14Other epistemic types include: 15\li \ref variables-continuous_interval_uncertain 16\li \ref variables-discrete_interval_uncertain 17\li discrete_uncertain_set \ref variables-discrete_uncertain_set-string 18\li discrete_uncertain_set \ref variables-discrete_uncertain_set-real 19 20<!-- 21\li discrete_uncertain_set \ref variables-discrete_uncertain_set-integer 22 23In addition to continuous and discrete aleatory probability 24distributions, %Dakota provides support for continuous and discrete 25epistemic uncertainties through the keywords: 26 27Interval-based and set variables do not represent probability distributions. 28--> 29 30Topics:: discrete_variables, epistemic_uncertain_variables 31Examples:: 32Let d1 be 2 or 13 and d2 be 4, 5 or 26. 33The following specification is for an interval analysis: 34\verbatim 35discrete_uncertain_set 36 integer 37 num_set_values 2 3 38 set_values 2 13 4 5 26 39 descriptors 'di1' 'di2' 40\endverbatim 41 42Theory:: 43The \c discrete_uncertain_set-integer 44variable is NOT a discrete random variable. 45It can be contrasted to a the histogram-defined random variables: 46\ref variables-histogram_bin_uncertain and \ref variables-histogram_point_uncertain. 47It is used in epistemic uncertainty analysis, where one is trying to model 48uncertainty due to lack of knowledge. 49 50The discrete uncertain set integer variable is used in both interval analysis 51and in Dempster-Shafer theory of evidence. 52 53\li interval analysis 54-the values are integers, equally weighted 55-the true value of the random variable is one of the integers in this set 56-output is the minimum and maximum function value conditional 57on the specified inputs 58 59\li Dempster-Shafer theory of evidence 60-the values are integers, but they can be assigned different weights 61-outputs are called "belief" and "plausibility." 62Belief represents the smallest possible probability that is consistent with the evidence, 63while plausibility represents the largest possible probability that is consistent with the evidence. 64Evidence is the values together with their weights. 65 66Faq:: 67See_Also:: 68