Dakota Reference Manual: histogram_point_uncertain

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histogram_point_uncertain

Aleatory uncertain variable - discrete histogram

## Topics

This keyword is related to the topics:

- discrete_variables
- aleatory_uncertain_variables

## Specification

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

## Description

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.

- the `x` values must be strictly increasing (lexicographically for strings).

- all `c` values must be positive.

- a minimum of one pair must be specified for each point-based histogram.

## Examples

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).

## See Also

These keywords may also be of interest:

- histogram_bin_uncertain

## FAQ

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).