conditional probability chain rule? I am aware of the general conditional probability rule which says that
$P(ABCD) = P(A|BCD)P(B|CD)P(C|D)P(D)$
But is there any situation where one can write
$P(A|D) = P(A|B)P(B|C)P(C|D)$ where $A,B,C,D$ are random variables.
Thanks

This works with Markov chains.  It's essentially the definition of a Markov chain.
