Causal Markov condition

The Markov condition, sometimes called the Markov assumption, is an assumption made in Bayesian probability theory, that every node in a Bayesian network is conditionally independent of its nondescendents, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it. This is equivalent to stating that a node is conditionally independent of the entire network, given its Markov blanket. The Markov condition, sometimes called the Markov assumption, is an assumption made in Bayesian probability theory, that every node in a Bayesian network is conditionally independent of its nondescendents, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it. This is equivalent to stating that a node is conditionally independent of the entire network, given its Markov blanket. The related Causal Markov (CM) condition states that, conditional on the set of all its direct causes, a node is independent of all variables which are not direct causes or direct effects of that node. In the event that the structure of a Bayesian network accurately depicts causality, the two conditions are equivalent. However, a network may accurately embody the Markov condition without depicting causality, in which case it should not be assumed to embody the causal Markov condition. Let G be an acyclic causal graph (a graph in which each node appears only once along any path) with vertex set V and let P be a probability distribution over the vertices in V generated by G. G and P satisfy the Causal Markov Condition if any node X in V is independent of D e s c e n d a n t s ( X ) { extstyle Descendants(X)} given P a r e n t s ( X ) . { extstyle Parents(X).} Statisticians are enormously interested in the ways in which certain events and variables are connected. The precise notion of what constitutes a cause and effect is necessary to understand the connections between them. The central idea behind the philosophical study of causation is that causes raise the probabilities of their effects, all else being equal. A deterministic interpretation of causation means that if A causes B, then A must always be followed by B. In this sense, smoking does not cause cancer because some smokers never develop cancer. On the other hand, a probabilistic interpretation simply means that causes raise the probability of their effects. In this sense, changes in meteorological readings associated with a storm do cause that storm, since they raise its probability. (However, simply looking at a barometer does not change the probability of the storm, for a more detailed analysis, see: ).