15.3 Information Combination as a BN Design Pattern 361
independent uniform distributions for all of the other nodes. As we noted
earlier, a uniform distribution adds no information to an information com-
bination process. In general, the evidence can be a BN. In other words, one
can combine two independent BNs. However, the combined JPD need not
have the same graph as the BNs that were combined, even when the original
two BNs have the same graph. This is a consequence of Berkson’s paradox.
However, if the BNs are measurements from the same population and have
the same graph, then the combined BN should also have the same graph. In-
deed, if it does not, then this is evidence that the original BNs were not from
the same population.
Summary
- The continuous information combination theorem gives the formula for
fusing independent continuous random variables that measure the same
phenomenon.
- The derivation of an a posteriori distribution from an a priori distribu-
tion and an observation is a special case of the information combination
theorems.
- Stochastic inference in a BN is another special case of the information com-
bination theorems.
15.3 Information Combination as a BN Design Pattern
Figure 15.1 Information combination as a BN pattern. Two or more independent
observations are combined to produce a single probability distribution.
The combination of independent sources of evidence can be expressed as
the BN pattern shown in figure 15.1. This pattern differs from the reconcilia-
tion pattern discussed in subsection 14.3.5. In the reconciliation pattern, the
