mutual_info

Calculate the mutual information between prior and posterior

Specification

• Alias: None

• Arguments: 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 $X$ and $Y$ , the mutual information is

$$I(X,Y)=\int \int p(x,y)\log \frac{p(x,y)}{p(x)p(y)}dxdy.$$

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 $k$ -nearest neighbor approximation algorithm. As of Dakota 6.6, there are two such algorithms available, both of which are derived in [KStogbauerG04] . 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 theory section section of the User’s Guide.

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.