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Causal Inference with Bayesian Networks
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A Bayesian network is a factored representation of a complete probability distribution according to a directed acyclic graph . A BN satisfies the local Markov property that every node in graph is conditionally independent of all its nondescendants, given all its parents in the distribution .
The graphical condition of d-separation between disjoint subsets of nodes , and means that nodes in block all paths between nodes in and nodes in. A path is blocked if it travels through a node in whose incident edges are non-colliding, or it passes through a collider node, but that node and all its descendants are outside . By edges colliding, we mean that the direction of the arrows is in opposing directions.
We use the notation to denote all triples such that d-separates and in , to denote all triples such that is conditionally independent of given in ,
A Bayesian network satisfies the global Markov property if is a subset of and we say is an I-map for or that and are...