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not necessarily conditionally independent given C,
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not necessarily conditionally independent given C,
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 not necessarily independent
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 not necessarily independent
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 not necessarily independent
IntroBNsPublic_Page_04
 not necessarily independent
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 not necessarily independent
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Watch outfor thisstatement!
Bayes’ Ball: The Rational Pastime  (Shachter98)
Correct algorithm:
Shade in evidence
Start ball at source node
Try to reach target by passing ball
States: pair of (node X, previousstate S)
Successor function (includingbounce back!):
X unobserved:
To any child
To any parent if coming from achild
X observed:
From parent to parent
If you can’t reach a node, it’sconditionally independent of thestart node given evidence
S
X
X
S
S
X
X
S
x
x
x
x
x
x
x
x
Example
R
T
B
D
L
T’
Example
R
T
B
D
L
T’
Yes
Example
R
T
B
D
L
T’
Yes
Yes
Example
R
T
B
D
L
T’
Yes
Yes
No
Example
R
T
B
D
L
T’
Yes
Yes
No
No
Deriving Useful Properties
Which nodes are(unconditionally) independent ofS?
bn
bn
Deriving Useful Properties
Which nodes are(unconditionally) independent ofS?
Nodes w/o common ancestors
bn-ind2
Deriving Useful Properties
Which nodes are(unconditionally) independentof S?
Nodes w/o common ancestors
Which nodes are conditionallyindep. ofS given S’s parents?
bn-parents
bn
parents
Deriving Useful Properties
Which nodes are(unconditionally) independentof S?
Nodes w/o common ancestors
Which nodes are conditionallyindep. ofS given S’s parents?
All nondescendants
 
bn
bn-blanket
Deriving Useful Properties
Which nodes are(unconditionally) independentof S?
Nodes w/o common ancestors
Which nodes are conditionallyindep. ofS given S’s parents?
All nondescendants
Given S’s Markov Blanket?(parents, kids, kids’ parents)
bn
markov-blanket
Deriving Useful Properties
Which nodes are(unconditionally) independentof S?
Nodes w/o common ancestors
Which nodes are conditionallyindep. ofS given S’s parents?
All nondescendants
Given S’s Markov Blanket?(parents, kids, kids’ parents)
All other nodes!
bn
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= same set of conditional independent statements
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= same set of conditional independent statements
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= same set of conditional independent statements
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Not a distribution!
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Not a distribution!
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Not a distribution!
Judea Pearl’s do-calculus
Infer effect of setting D
http://www6.pcmag.com/media/images/338302-judea-pearl.jpg?thumb=y
Influence Diagram
P(R|FD = d) =