Dakota Reference Manual: mutual_info

| Dakota Reference Manual Version 6.15 Explore and Predict with Confidence

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mutual_info

Calculate the mutual information between prior and posterior

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Optional | ksg2 | Use second Kraskov algorithm to compute mutual information

## Description

The mutual information quantifies how much information two random variables contain about each other. It is a measure of the mutual dependence of two random variables. The mutual information is a non-negative measure, with zero representing complete independence of the two random variables. For continuous random variables and , the mutual information is

The mutual information can also be interpreted as the reduction in uncertainty of one random variable due to the knowledge of another. By specifying, `mutual_info`, the mutual information between the posterior parameters and the prior parameters is calculated.

The mutual information is calculated using a -nearest neighbor approximation algorithm. As of Dakota 6.6, there are two such algorithms available, both of which are derived in[58] . By default, Dakota uses the first such algorithm; the second may be selected by specifying the keyword `ksg2`. Further details can be found in the Dakota Theory Manual [15] .

Expected Output

If `mutual_information` is specified, the calculated value will be reported to the screen at the end of the calibration.

Additional Discussion

Due to the necessary approximation of the multidimensional integral above, a negative mutual information may be reported for applications whose true value is close to or equal to zero. As of Dakota 6.6, mutual information calculations are primarily used in the implementation of the experimental_design algorithm.

## Examples

    method
        bayes_calibration queso
          dram
          seed = 34785
          chain_samples = 1000
          posterior_stats mutual_info