Bernal S D_2010.pdf - University of Plymouth

3 J. DEFINITION AND MATHEMATICAl. FORMULATION
Note the Xx{ui) message can be sent to node U, as soon as messages from all other
nodes, except node Uj, have been received. Analogously %^ (j;) can be sent as soon as all
messages, except that arriving from node Cj, have been received,
3.3.3.6 Boundary conditioiLs and evidence nodes
There are four types of nodes that are considered special cases and need to be initialized as
follows:
1. Root nodes: For a node X without parents, n{x) is set equal to the prior probability P{x).
2. Aniicipatoiy nodes: I-or a node X without children, which has not been instantiated, X{x)
is set equal to u flat disiribulion (1,1 I), so thai liel{x) is equal lo n{x).
3. Evidence nodes: For a node X Ihat has been instantiated, such Ihat the /-Ih value of X is
observed to be Irue. X{x) is set equal to (0 0,1,0, ...0) with 1 at the _/-lh ptisilion. This
is usually referred to as hard evidence.
4. Dummy nodes: A nodcX can receive virtual or judgmental evidence from a child dummy
node C. In this case the X[c) and n{c) do not exist, but instead a Xc{x) message from
Clo X is generated where Xc-[x") = p • P{ohsfrvalion\x). The observation can consist of
any probability distribution over the states of node X, and is usually referred to as soft
evidence.
3.3 J.7 Example of hcliel' prupagation with diagnostic evidence
When evidence occurs in the child node and propagates to the parent node, from known effects
to unknown causes, this is denoted as diagnostic reasoning or bonom-up recognition. Figure 3.6
shows a scenario, based on the previously described toy example, where evidence about Surfing
propagates across the network, updating the beliefs in all other nodes.
Note that because variables arc binary, the pwbability ofX or the belief of X refer lo the proba­
bility of variable X being in the true state.
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