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causality. In particular, the concern was to distinguish causality from corre-
lation. A number of books have appeared that deal with these issues such
as one by Pearl (Pearl 2000) who originated the notion of BNs. For causation
in biology, see (Shipley 2000). Other books that deal with this subject are
(Glymour and Cooper 1999; Spirtes et al. 2001).
Summary
- A BN is a graphical mechanism for specifying JPDs.
- The nodes of a BN are random variables.
- The edges of a BN represent stochastic dependencies.
- The graph of a BN must not have any directed cycles.
- Each node of a BN has an associated CPD.
- The JPD is the product of the CPDs.
14.2 Stochastic Inference
The main use of a BN is to perform inference. This is done by observing some
of the random variables. One can then query the BN to determine how the
distributions of other random variables are affected. Specifying known facts
is done by giving the values of some of the random variables. The values can
be given as actual crisp values or as a PD on the values. The nodes that have
been given values are termed theevidence. One can then choose one or more
of the other nodes as thequerynodes. The answer to the query is the JPD of
the query nodes given the evidence.
Inference in a BN is analogous to inference performed by a rule engine.
Recall from section 3.1, that in a rule engine one specifies a collection of if-
then rules, called the rule base. One can then input a collection of known
facts (typically obtained by some kind of measurement or observation). The
rule engine then explicitly (as in a forward-chaining rule engine) or implicitly
(as in a backward-chaining rule engine) infers other facts using the rules.
The set of specified and inferred facts form the knowledge base. One can
then query the knowledge base concerning whether a particular fact or set
of facts has been inferred. A BN is analogous to a rule base. The evidence
presented to a BN is analogous to the facts initially specified in a rule engine.
Both BNs and knowledge bases can be queried.
