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I am looking at a description of a process that says

$f(y|a_1,z,a_0) = \dfrac{f(y,a_1,z,a_0)}{p(a_1|z,a_0)p(z|a_0)p(a_0)}$

I am not sure if I follow this joint pdf, conditical pdf , p(.) relation. Need help understanding this with an example.

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This looks to be a version of the probability chain rule. Since $f(y, a_0, z, a_1) = f(y | a_0, z, a_1) \times p(a_1 | z, a_0) \times p(z | a_0) \times p(a_0)$. You can divide through by the last three terms in my equation to arrive at your equation.

https://en.wikipedia.org/wiki/Chain_rule_%28probability%29#More_than_two_random_variables

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  • $\begingroup$ ah thanks for this suggestion. Gives me something to dig deeper . $\endgroup$ – Sundown Brownbear Mar 29 at 13:48

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