14.3 Constructing Bayesian Networks 349
called “noisy OR-gate” models the combining of evidence in favor of a sin-
gle conclusion, as shown in figure 14.5 (Pearl 1988). The evidence nodes and
conclusion are all modeled as random variables that are either true or false.
Each evidence node that is true increases the likelihood that the conclusion
is true, and vice versa. If all of the evidence nodes are false, then the con-
clusion is certain to be false. Each evidence node can contribute a different
amount to the conclusion, and the evidence nodes contribute independently
to the conclusion. figure 14.5 shows how the conditional probability table
is defined for a noisy OR-gate. In this figure, the amount that an evidence
nodeXcontributes to the conclusion is 1 −qX. If this parameter is equal
to 1, then the truth of the corresponding evidence node is conclusive: the
conclusion is true with probability 1. In practice, evidence nodes will have
much smaller contributions. Other “noisy” operations include noisy-AND,
noisy-MAX and noisy-MIN operations (Pradhan et al. 1994).
Figure 14.5 The noisy OR-gate BN design pattern.Other authors have mentioned patterns that may be regarded as being de-
sign patterns, but in a much more informal manner. For example in (Murphy
1998) quite a variety of patterns are shown such as the BNs reproduced in
figure 14.6. In each of the patterns, the rectangles represent discrete nodes
and the ovals represent Gaussian nodes. The shaded nodes are visible (ob-
servable) while the unshaded nodes are hidden. Inference typically involves
specifying some (or all) of the visible nodes and querying some (or all) of the
hidden nodes.
A number of Design idioms for BNs were introduced by (Neil et al. 2000).
The definitional/synthesis idiom models the synthesis or combination of
many nodes into one node. It also models deterministic definitions. The
cause-consequence idiom models an uncertain causal process whose conse-
quences are observable. The measurement idiom models the uncertainty of
a measuring instrument. The induction idiom models inductive reasoning
based on populations of similar or exchangeable members. Lastly, the rec-