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bilistic relationship among a set of variables (Pearl 1988). A BBN is repre-
sented with a directed acyclic graph (DAG), where nodes represent variables
of interest (vertical irregularity, exposure, etc.), and the links between them
indicate informational or causal dependencies among the variables (Pearl
1988; Straub and Der Kiureghian 2010a,b). The absence of a link between
two variables is an indication of conditional independence between the
corresponding variables.
Uncertainties in a BBN model are described through subjective probabil-
ity (Pearl 1988). As depicted in Fig. 7.1, a BBN is composed of:
•
a set of variables (e.g.
A
1
,
A
2
and
B
3
) and a set of directed links between
the variables;
•
a set of mutually exclusive states for each variable (e.g. for
A
1
and
A
2
the states are {L, M, H}); and,
•
an assigned conditional probability for each variable with 'parents' (e.g.
for
B
3
).
The relations between the variables in a BBN are expressed in terms of
family relationships, where a variable
A
1
is said to be the parent of
B
3
and
B
3
the child of
A
1
if the link goes from
A
1
to
B
3
(Fig. 7.1). The dependence
Variable
A
1
Variable
A
2
Variable
A
1
Probability
Variable
A
2
Probability
L
P
(
A
1
= L)
L
M
H
P
(
A
2
= L)
M
P
(
A
1
= M)
P
(
A
2
= M)
P
(
A
2
= H)
H
P
(
A
1
= H)
Unconditional
probability (UP)
Variable
B
3
Unconditional
probability (UP)
Variable
B
3
Variable
A
1
Variable
A
2
Probability
L
M
H
L
L
P(
B
3
= L
⏐
A
1
= L,
A
2
= L)
P(
B
3
= M
⏐
A
1
= L,
A
2
= L)
P(
B
3
= H
⏐
A
1
= L,
A
2
= L)
…
…
…
…
…
H
M
P(
B
3
= L
⏐
A
1
= H,
A
2
= M) P(
B
3
= M
⏐
A
1
= H,
A
2
= M)
P(
B
3
= H
⏐
A
1
= H,
A
2
= M)
H
H
P(
B
3
= L
⏐
A
1
= H,
A
2
= H) P(
B
3
= M
⏐
A
1
= H,
A
2
= H)
P(
B
3
= H
⏐
A
1
= H,
A
2
= H)
Conditional probability table (CPT)
7.1
Schematic of a Bayesian belief network.
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