Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Aleatory uncertain variable  discrete histogram
This keyword is related to the topics:
Alias: none
Argument(s): none
Default: no histogram point uncertain variables
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  integer  Integer valued point histogram variable  
Optional  string  String (categorical) valued point histogram variable  
Optional  real  Real valued point histogram variable 
Histogram uncertain variables are typically used to model a set of empirical data. When the variables take on only discrete values or categories, a discrete, or point histogram is used to describe their probability mass function (one could think of this as a histogram_bin_uncertain variable with "bins" of zero width). Dakota supports integer, string, and realvalued point histograms.
Point histograms are similar to discrete_design_set and discrete_state_set, but as they are uncertain variables, include the relative probabilities of observing the different values within the set.
The histogram_point_uncertain
keyword is followed by one or more of integer
, string
, or real
, each of which specify the number of variables to be characterized as discrete histograms of that subtype.
Each discrete histogram variable is specified by one or more abscissa/count pairs. The abscissas
, are the possible values the variable can take on ("x" coordinates of type integer, string, or real), and must be specified in increasing order. These are paired with counts
c
which provide the frequency of the given value or string, relative to other possible values/strings.
Thus, to fully specify a pointbased histogram with n
points, n
(x,c) pairs must be specified with the following features:
x
is the point value (integer, string, or real) and c
is the corresponding count for that value.x
values must be strictly increasing (lexicographically for strings).c
values must be positive.The pairs_per_variable
specification provides for the proper association of multiple sets of (x,c) or
(x,y) pairs with individual histogram variables. For example, in the following specification,
histogram_point_uncertain integer = 2 pairs_per_variable = 2 3 abscissas = 3 4 100 200 300 counts = 1 1 1 2 1
pairs_per_variable
associates the (x,c) pairs {(3,1),(4,1)} with one pointbased histogram variable (where the values 3 and 4 are equally probable) and associates the
(x,c) pairs {(100,1),(200,2),(300,1)} with a second pointbased histogram variable (where the value 200 is twice as probable as either 100 or 300).
These keywords may also be of interest:
Difference between bin and point histograms: A (continuous) bin histogram specifies bins of nonzero width, whereas a (discrete) point histogram specifies individual point values, which can be thought of as bins with zero width. In the terminology of LHS[89], the bin pairs specification defines a "continuous linear" distribution and the point pairs specification defines a "discrete histogram" distribution (although the points are realvalued, the number of possible values is finite).