Bernal S D_2010.pdf - University of Plymouth

3.3. DEFINITION AND MATHEMATICAl^ FORMULATION
= i;i,l)'(0.27,0.73)^(0.27,0.73)
K{W) - ^n^g,"!) • nw(g) • rcw[m)
n{w = 0) = {P{w ^ OIJ? = 0,m = 0) • iZv^iR - 0) • nw{m - 0)) +...
+ (^(^--01^- l,ffl = 0)-;riv(j?- I}-;rvv(m-0)) + ...
+ {P{w = 0[^' = 0.;/i = I) • ^TivC^ - 0). TTivlm - 1)) + ...
+ {P{w = Q\g= \.m= \)-nw{g= \)-nw(m= \))
-(0.9 0.8 0.5)+ (0.2-0.2-0.5)+ (0.3 0.8-0.5)+ (0.9'0.2-0.5)-0.51
n{w - 1) = (0.1 0.8 • 0.5) + (0.8 • 0.2 • 0.5) + (0.7 • 0.8 • 0.5) + (0.9 • 0.2 • 0.5) - 0.49
;r(>v)-(0.51,0.49)
Bel{w) - a-X{w)-n{w)
-a(0.27,0.73)-(0.51,0.49)-ct-(0.138,0.358)
^(0.278,0.722)
In this case, the evidence in Surfing yields a value of k{w) that suggests there is a high prob­
ability of Waves (0.73). The top-down prior information i:{w) is practically a flat distribution
(0.51,0.49), i.e. doesn't add any inforniaiion. ihu.s the resulting Ixilief suggests there is u high
probability of Waves (0.722). This is shown graphically in the top diagram of Figure 3.6.
The next step is to generate the outgoing messages from node IV to its child and parent nodes.
The key property here is that the outgoing messages take into account all evidence except that
which originated from the destination node. For example, the message from W to G. An'(^),
doesn't take into account the prior information conveyed through the incoming message Ttwig).
Given Equations (3.30) and (3.31). the resulting expressions are
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