Bernal S D_2010.pdf - University of Plymouth

3.3. OmNmON AND MATHEMATSOALFORMVLATION
Xw(g ^ 0) = A(M' = 0} • {P(w = 0\g = O.m = 0) • Kwim - 0) + ...
+ />(» - 0|JE; - 0,m - 1) • nwim = 1)) + ...
+ A(M'^ {)-{P[W= l|g-O,m-O)-;rw(m = 0) + ...
+ P[w^ l|i'-0,m- I)-;rw(m-l))
-0.27-(O.9-0.5 + 0.3-0.5)+O.73(O.|.0.5 + 0.7-0.5) =0.454
Xy^{^ = I) = 0.27 • fO.2 -0.5 + 0.1 -0.5) + 0.73 • (0.8 • 0.5 -f 0.9 • 0.5) - 0.661
AwU) - ^ • (0.454.0.661) = (0.407,0.593)
^iv('")-^'^A(H')£P(iv|^.ffl)-;rH.(^)
11 in
Atv(m = 0) = 0.27-(0.9-0.8 + 0.2-0.2) +0.73 • (0.1 -0.8 + 0.8 0.2) - 0.38
^[m =\) = 0.27 • (0.3-0.8 + 0.1 -0.2) +0.73 • (0.7 -0.8 + 0.9 0.2) - 0.61
AH.(/M) = i3-(0.38,0.61) = (0.384,0.616)
nf{w) - (i • ks{w) • 7i{w)
= j5 • (0.27,0.73) • (0.51,0.49) ^ /J(0.138,0.358) = (0.278,0.722)
ns{w)^ji-XF{w)-n{w)
= ^-{l.l)-(0.5l,0.49) = (0.51,0,49)
Note how the bottom-up messages. Xw {g) and X}\i{m), take into account, not only the bottom-up
evidence, but also the prior probability conveyed by the parent node to which the message is not
destined. This is sometimes referred lo as horizonial or sideways interactions between parent
nodes with a common successor, and results in the explaining away effect. Analogously, the lop-
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