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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

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    Try $A\subseteq B\subseteq C\subseteq D$.2012-02-13
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    @suresh Per [faq](http://math.stackexchange.com/faq#signatures), usage of signature is not recommended, so I removed it.2012-02-13
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    @Sasha, I was not aware of this. Thanks for pointing it out2012-02-13
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    @MichaelGreinecker how? i didnt get it?2012-02-13
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    Actually, you'd want $A,B,C,D$ to be _events_ rather than random variables.2012-02-13
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    In general, you run into the problem that you can have both events $A$ and $D$ occur without $B$ and $C$ occuring. If the events are nested, this problem can not occur.2012-02-13

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