Arrows on the path meet either head to tail or tail

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1.arrows on the path meet either head-to-tail or tail-to-tail at the node and this node is in Z 2.the arrows meet head-to-head at the node, and neither the node, nor any of its descendants, is in Z X1 indep of X3 given X2? X3 indep of X1 given X2? X4 indep of X1 given X2? X1 X4 X2 X3 X and Y are D-separated by Z (and therefore conditionally indep, given Z) iff every path from any variable in X to any variable in Y is blocked by Z A path from variable A to variable B is blocked by Z if it includes a node such that either 1.arrows on the path meet either head-to-tail or tail-to-tail at the node and this node is in Z 2.the arrows meet head-to-head at the node, and neither the node, nor any of its descendants, is in Z X4 indep of X1 given X3? X4 indep of X1 given {X3, X2}? X4 indep of X1 given {}? X1 X4 X2 X3
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16 X and Y are D-separated by Z (and therefore conditionally indep, given Z) iff every path from any variable in X to any variable in Y is blocked A path from variable A to variable B is blocked if it includes a node such that either 1.arrows on the path meet either head-to-tail or tail-to-tail at the node and this node is in Z 2.the arrows meet head-to-head at the node, and neither the node, nor any of its descendants, is in Z a indep of b given c? a indep of b given f ? Markov Blanket from [Bishop, 8.2]
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17 What You Should Know Bayes nets are convenient representation for encoding dependencies / conditional independence BN = Graph plus parameters of CPD’s Defines joint distribution over variables Can calculate everything else from that Though inference may be intractable Reading conditional independence relations from the graph Each node is cond indep of non-descendents, given only its parents – D-separation ‘Explaining away’ See Bayes Net applet:
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  • Fall '11
  • Mitchell,Tom
  • Probability theory, Bayesian network

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