$P(X|Y) = \prod_{i=1}^{n} P(X_i|Y)$

Question

What is the interpretation of such statement: $$\mathbb P(X|Y) = \prod_{i=1}^{n} \mathbb P(X_i|Y)$$ where $X=(X_1, X_2, ..., X_n)$?

Answer 1

It means that $X_1, ... X_n$ are conditionally independent given $Y$.

Answer 2

To add to the other answer and comment, here is a Bayesian graph to represent your scenario:

Resources for further information:

• https://en.wikipedia.org/wiki/Bayesian_network
• https://ermongroup.github.io/cs228-notes/representation/directed/