Mean, Value, and Standard Deviations

For Continuous Nodes or Discrete Nodes with numerical states, a Monitor displays the following items:

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The Expected Value $v$ (Value) is shown in all Monitors, regardless of the node type (categorical or numerical).
The Mean Value $m$ (Mean) and its Standard Deviation (Dev) are displayed only in the Monitors of numerical nodes.

Examples

Categorical Node

Consider the discrete node $Age$ with three categorical Node States:

Child
Adult
Senior

Categorical Node with Assigned State Values

In the Node Editor, you can assign State Values to the Node States of $Age$ .

For each node, the Expected Value $v$ is computed using the assigned State Values and the marginal probability distribution of the Node States:

v = \sum_{s \in S} p_s \times V_s

Where $p$ is the marginal probability of state $s$ and $V_s$ is its associated value.

v = 0.23 \times 10 + 0.415 \times 40 + 0.355 \times 70 = 43.750

The Monitor shows $v$ as the Value of $Age$ .

The Monitor of a categorical node does not show a Mean value.

Discrete Numerical Variable

Suppose the node $Age$ has three numerical Node States instead of categorical ones.

No State Values Specified

If State Values are not specified in the Node Editor, BayesiaLab uses the numerical values of the Node States as the State Values.

The Mean $m$ is computed using the numerical values of the Node States and their marginal probabilities:

m = \sum_{s \in S} p_s \times c_s

Where $c_s$ is the numerical value of the Node State.

m = 0.23 \times 10 + 0.415 \times 40 + 0.355 \times 70 = 43.750

In this case, Mean and Value are identical.

State Values Specified

If State Values are specified in the Node Editor, they are used to calculate Value.

The Expected Value $v$ is calculated as:

v = \sum_{s \in S} p_s \times V_s

Where $V_s$ is the assigned State Value.

v = 0.23 \times 0 + 0.415 \times 1 + 0.355 \times 2 = 1.125

In this case, Mean and Value are not identical.

Continuous Numerical Variable

For a continuous variable Age defined in the domain [0; 99], discretized into three states:

Child: [0; 18]
Adult: ]18; 65]
Senior: ]65; 99]

The Monitor displays Mean (m), Standard Deviation (Dev), and Expected Value (v).

Value Delta

If evidence modifies the node’s distribution, the Monitor displays a delta value next to Value:

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

The Expected Value before evidence was set.
The Reference Probability Distribution.

Special Case: Some Node States Without Values

If only some Node States have values, the Expected Value $v$ is computed from the subset $S^*$ of Node States with values:

v = \sum_{s \in S^*} \frac{p_s}{P^*} \times V_s

If only one Node State has a value, the Monitor does not report $v$ .