Examples of Equation Use
Here are example equations for some common or non-obvious situations:
State Comparisons: Suppose the states of node Source are CA, TX, FL, BC and NY. The states of node Dest are TX, NY, MA and UT. We want to know if cross-border travel is required to transport from Source to Dest, and that is indicated by the = 4 && typeof(BSPSPopupOnMouseOver) == 'function') BSPSPopupOnMouseOver(event);" class="BSSCPopup" onclick="BSSCPopup('X_PU_boolean_node.htm');return false;">boolean node Travel. The equation below works even though nodes Source and Dest have different sets of states, and in a different order.
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Travel (Source, Dest) = (Source != Dest) |
Additive Noise: Say you want to represent something like:
x1 = x2 + gauss (0, 0.2) which could indicate that x1 is the same as x2, but with the addition of Gaussian noise having mean 0 and s = 0.2. You could do this by defining a new node x3, and setting the equations of x1 and x3 as:
x1 (x2, x3) = x2 + x3
p(x3) = NormalDist (x3, 0, 0.2)
Multiple Discretizations: Sometimes it is useful to use more than one node to represent a continuous variable, and discretize each differently. For example, the coarser one may be a parent for another node whose CPT would be too big with a finer discretization, while the finer one would serve as a parent for nodes requiring more accuracy. Put a link from the finer node to the coarser, and give the coarser node an equation like:
X_d4 (X_d12) = X_d12
Noisy-Or: To create a noisy-or node, just create a regular = 4 && typeof(BSPSPopupOnMouseOver) == 'function') BSPSPopupOnMouseOver(event);" class="BSSCPopup" onclick="BSSCPopup('X_PU_boolean_node.htm');return false;">boolean nature node, put links to it from the possible causes, give it a noisy-or equation, and use that to build its CPT. For extra computational efficiency you may want to select it and choose Modify → Decompose Equations before building the CPT.
For example, if C1, C2 and C3 are = 4 && typeof(BSPSPopupOnMouseOver) == 'function') BSPSPopupOnMouseOver(event);" class="BSSCPopup" onclick="BSSCPopup('X_PU_boolean_node.htm');return false;">boolean nodes representing causes of boolean node E, and there are links from each Ci to E, then E could have the noisy-or equation:
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P (E | C1, C2, C3) = |
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NoisyOrDist (E, 0, C1, 0.5, C2, 0.3, C3, 0.1) |
For its meaning, see the NoisyOrDist description. The causes, and even the link parameters, can be more complex expressions (then you won’t be able to use Modify → Decompose Equations though).
For example:
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P (Bond | Temperature, BackTemp, Pressure, Switch,Eff)= |
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NoisyOrDist (Bond, 0.001, |
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Temperature > BackTemp, 0.5, |
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Pressure == high, 0.3, |
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Switch, 0.9 * Eff) |