Hi I'm working with particle filters at the moment however my maths isnt so strong i was wondering given the $P(X_n|Y_0,....Y_{n-1})$ and $P(Y_n|X_n)$ how do you obtain $P(Y_n|Y_0,...,Y_{n-1})$? i.e. the equations that links the two?
Thanks
2026-04-12 16:56:17.1776012977
Probability Question - Conditional Probability
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Hint:
$P(B) = \sum_C P (B C) = \sum_C P(B | C) P(C)$
Hence (conditioning everything over A),
$P(B | A) = \sum_C P(B | C A ) P(C |A)$
You can't simplify this further, but in some cases (I'd bet in yours), depending on extra properties of the variables, you can assume that $P(B|C A) = P(B | C)$