is not observed due to the active trail .Therefore,. Since all such parents must appear before
in any topological order of
G
, all of them must be in
Moreover, for each child of,
that appears
before
in the topological order, we also know that
when
is not observed due to the active trail,
therefore. We know that we need to consider the coparents of
Xi
as well. Let’s consider a coparent
of, , that appears in the topological order before . As the name implies, is a parent of,
which is a
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sibling of. In, we have the following independency
, and
is a parent of
in . However, we are now
creating an independency that is NOT in
G
, since observing
will connect and
via an active trail in
G
that passes though , therefore,
cannot be dseparated from
using the current parent set of Since
each element of this parent set is necessary, we must add all such
as parents of to avoid creating
these extra independencies. These variables are now in fact necessary and sufficient replacement of
Xi
in
parenting
. In fact, we know that these variables are subset of the Markov Blanket of
Xi
,
namely, they are the variables in the
that appear in the topological order before. These variables
shield
from other variables in the network, thus using them to replace
no other active trail can
reach
and continue to
when these variables are observed. Therefore, using this set of new parents,
the local Markov assumption is satisfied for
in. We can explicitly create as follows
:
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 Spring '13
 Dr.ZAre
 Probability theory, Pearson productmoment correlation coefficient, active trail, G. Therefore, G. Moreover, Soheila Molaei

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