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362 15 Combining Information

dependency arrows are in the opposite direction. The conditional probabil-

ity distributions that define the BN for information combination are shown

in figure 15.2. The process of combining information from multiple sources is

a special case of stochastic inference. The random variables to be combined

(calledXandYin the figure) are given as evidence to the BN. Then query

the BN to obtain the combined random variableZ.

Figure 15.2 The conditional probability distributions that define the BN for combin-

ing two independent observations of the same phenomenon. The prior probability

distribution on theZis the uniform distribution.

Expressing information combination as a BN allows one to formulate more

general information combination processes. For example, one can combine

random variables that are dependent on each other or on common informa-

tion, or one can combine random variables that are not directly observable,

as shown in figure 15.3.

Summary

• The information combination process can be expressed as a BN.


• When expressed as a BN, information combination is a form of stochastic
  inference.


• The BN formulation of information combination allows one to formulate
  many information combination processes as well as other ways to com-
  bine information.