Bernal S D_2010.pdf - University of Plymouth

3.3. DEFINITION AND MATHEMATICAL FORMULATION
n(x) = P{x\et)
= Y^P{x\u)-P{u\4)
u
= Y,P{x\ii)-7lxiu) (3.20)
where P{x\u) is the conditional probability distribution stored on the link V —> X: and %(H) =
/'[it'lc^). represents how probable the value u is, based on causal evidence above the link U —> Jf.
jrx(w) can be understood as a message that node X receives from ils parent, which, multiplied
by the conditional probability Tunction that relates both nodes, yields the n{x) function.
In the more general case where multiple parents are present, we assume the evidence can be
partitioned such thai cj - e^^y UeJ^;^ U ... Ue^^.j^ (Figure 3.4). Therefore.
Jtix) = Pix\4)
= n^Kx 4,x)
= £ Pi^l" I'N)-P(U\ »N\tu,x *^u^x)
U]....,tlK
= Y, P{x\ut.....,UN)-P{i,t\e^^xy^-'-P("'^K,x)
Ul UN
"I "N
H|,. ..IIH l=i..S
where P(X\II\....,UM) represents the conditional probability distribution that relates node X to
88