Bernal S D_2010.pdf - University of Plymouth

3.3. DEFINITION AND MATHEMATICAL FORMULATION
• Serial connections: For example, the conneclion Af —» W —^ S in Figure 3.2. Node S is
condilionally dependent on mxle IV, and node W is conditionally dependent on node M.
This means entering evidence at nodes M or S will update the prnbabilily distribution or
node W. However, entering hard evidence in node W blocks or direttionally separates
{d-separates) nodes M and S.
In other words, nodes M and ,S are condilionally independent given hard evidence in node
W, also written as A/ Jl 5 | W. Thus, information may flow through serial connections
unless (he stale of the middle variable iW) is known. Inluitively speaking, given that we
already know the size of the waves (W), the moon alignmenl [M) does nol alTeci ihe
presence of surfing activity (S).
• Diverging connections: For example, ihe conneclion /*' .? in Figure 3.2, Child
nodes F and S are conditionally dependent on parent node W, thus entering evidence on
W will modify the probability dislribulion in nodes F and S. However, knowing the state
of W blocks {d-separates) nodes F and .V.
Therefore, nodes F and S are conditionally independeni given hard evidence al node W,
i.e. F }LS \'W. Hence, information may flow along diverging connections, unless the
state of Ihe middle node W is known. Intuitively, if we don't know the state of the waves
(W). the presence of fishing activity (F) could provide us some information about the
presence of surling activity {S). However, once we know the exact slate of the waves
(W). the presence of lishing activity [F) does nol affect the presence of surfing activity
(5) and vice versa.
• Converging connections: For example, the connection G ~^W i- M \n Figure 3.2. Child
node IV is conditionally dependent on parent nixies G and M. lintering hard evidence al
node G will update node W but have no effect on node M. However, if some evidence
is already present in node IV, then entering information in any of the parent nodes G or
M will update lh