The Gaussian normal distribution function is defined on the complete real axis. Any Gaussian normal distribution function can be specified by its mean and variance parameter. In HUGIN, a continuous chance node can have a single Gaussian normal distribution function for each configuration of its discrete parents states (both discrete chance nodes and decision nodes). If a continuous chance node has one or more continuous chance node as parent, the mean can be linearly dependent of the state of the continuous chance node parents.
In figure 2 is shown an example of the specification of a Gaussian normal distribution function of a continuous chance node (C3) having one discrete chance node (C1) and one continuous chance node (C2) as parents (see figure 1).
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Figure 1: An example of a Bbn where the continuous chance node C3 has one discrete chance node (C1) and one continuous chance node (C2) as parents. |
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Figure 2: The specification of a Gaussian normal distribution function for C3 having one discrete chance node (C1) and one continuous chance node (C2) as parents. |
This specification gives a Gaussian normal distribution function for each of the states of C1 (where N(m,v) is the Gaussian normal distribution function with mean m and variance v):
Only the mean depends linearly on a continuous parent node. The variance is constant for each configuration of the states of the discrete parents.