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Dakota Reference Manual
Version 6.15
Explore and Predict with Confidence
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Aleatory uncertain variable - discrete histogram
This keyword is related to the topics:
Alias: none
Argument(s): none
Default: no histogram point uncertain variables
Child Keywords:
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 real-valued 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 sub-type.
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 point-based 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 point-based 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 point-based 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 non-zero 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[93], the bin pairs specification defines a "continuous linear" distribution and the point pairs specification defines a "discrete histogram" distribution (although the points are real-valued, the number of possible values is finite).