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  • Target Mean Analysis with Soft/Hard Evidence

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Question

In the context of Target Mean Analysis (Validation Mode: Analysis | Visual | Target Mean Analysis), what does it mean to "Use Hard Evidence"?

Answer

The example below illustrates the difference between using Hard Evidence (box checked) and using Soft Evidence (box unchecked):

If "Use Hard Evidence" is selected, the points of the curve will correspond to the Values of the discrete states.

Example

The variable Pleasure has been discretized into 5 states. The values correspond here to the arithmetic means of the data points that are associated to each state.

The variable Intensity has 5 numerical values. Given that no values have been defined by the user, the values of the states are the numerical values of the variable.

The target mean analysis with these two nodes returns two curves made of five points.

The two points that are indicated in the graph correspond to the following hard evidence.

 


If Soft Evidence is selected (Hard Evidence unchecked), two kinds of evidence are used:

  • Hard evidence, for the extreme values (the min and the max),
  • Soft evidence (by setting target mean values) for the intermediate points. 

Intermediate points

Let n be the number of states of the node under analysis.

n+1 reference values are defined by using the values of the n states plus the expected value given the current marginal probability distribution of the variable.

These reference values define n intervals where intermediates points are equally distributed. By default, the number of intermediate points is three, but this value can be changed via the Settings (Options | Settings | Analysis | Target Mean Analysis).

Example

 

The graph below illustrates the reference values for the node Pleasure: the five values associated to the states plus the expected value given the marginal distribution (see the monitor). These six reference values define the five intervals depicted in green.