Bernal S D_2010.pdf - University of Plymouth

3.3. DEFINITION AND MATHEMATICAL FORMUI.ATION
Afler resioring ihe original meaning of V, such thai P{x\v.ui) ~ P{x\u\,...u\). and
the final expression is
pi^Hx)- n ^'("^Kx)- n 'r^f"*) (3.23)
k^\..N\i k=i..N\l
^X(M,) = ^L Mx) £ /'(.V|"I,.-."N) n '^^f"*)
HI,...,UN\((, k^\..N\i
(3.24)
where /3 is a normalizing constant, and A(x) is defined in Equation (3.24). Note, in the previous
derivation we assume nodes X and V themselves are not instantiated and are therefore not part
of the evidence setse^;^ and e^j^, respectively,
3.3.3.4 Top-down mcs.sa(>es
We now consider the generic message 7lCj(x) that node X sends to its child node Cj, as shown
in Figure 3.4. The body of evidence which must be sent in this message includes all evidence
available, except the evidence found in the subnetwork below the link X -t Cj, i.e. ej^ -
c-fixc,- Therefore. Tic^ix) is equivalent to the belief of X (Equation (3.18)) when the evidence
e^c is suppressed, which can be written as,
^M) = 4c Belix)
-a f] kc,{x)-n{x) (3.26)
*=l..M\j
where a is a normalizing constant, and n(x) is defined in Equation (3.20).
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