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• Means and Values of Nodes

# Question

How does BayesiaLab calculate the Means and Values in the Monitors? What is the difference?

For each node that has values associated with its states, an Expected Value  is computed by using the associated values and the marginal probability distribution of the node.

where  is the marginal probability of state  and  is its associated value.

This Expected Value is displayed in the monitor.

Example

Let's take a discrete node Age with three categorical states:

• Senior

The Node Editor allows associating numerical values with these states.

Let's suppose now that the variable Age has three numerical states.

As it's a numerical node, its monitor will have a Mean value, a Standard Deviation and an Expected Value.

When the states do not have any associated values, is automatically set to the numerical value of the state.

Otherwise, the state values defined by the user are used:

The Mean value m is computed with the following equation:

where  is the numerical value of the state.

Let's consider now a continuous variable Age defined on the domain [15 ; 99], and discretized into three states:

• Young Adult: [15 ; 30]
• Senior: ]60 ; 99]

Again, as it's a numerical node, its monitor will have a Mean value, a Standard Deviation and an Expected Value.

The Mean value m is computed with the following equation:

where  is the central tendency of the state defined as:

• the mid-range of the state when no data is associated,
• the arithmetic mean of the data points that are associated with the state.

When the states do not have any associated values, is automatically set to the central tendency of the state.

If a dataset is associated to a continuous variable, clicking on the Generate Values buttons sets the values to the current arithmetic means.

When new pieces of evidence are set, a the delta value is displayed in the monitor:

This delta is the difference between the current Expected Value  and:

• the previous one,
• the one corresponding to the reference probability distribution set with  in the toolbar.

When only some states have an associated value, the Expected Value is computed on the states that have associated values

where

When is only made of one state, the node is considered as not having any associated values.