Dakota Reference Manual  Version 6.4 Large-Scale Engineering Optimization and Uncertainty Analysis
histogram_point_uncertain

Aleatory uncertain variable - discrete histogram

## Topics

This keyword is related to the topics:

## Specification

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

## 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).