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Suppose I have a model $y = x + n$. The law of $x$ and $n$(noise) are known. $y$ is the observation.

Thus I write: $ p(y|x) = p_n(y-x)$.

Using the Bayes's rule I have: $p(x|y) \propto p(y|x) p(x) $.

However, why could I not write: $p(x|y) = p_n(y-x)$ ?

I know it is false but why ?

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  • $\begingroup$ Your fourth line seems to ignore the $p(x)$ you have in your third line $\endgroup$
    – Henry
    Commented May 28, 2016 at 1:00

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