In MAP estimation for linear regression task, the posterior of the weight given the data is written as $p(w|X,Y)=\frac{p(Y|X,w)p(w)}{p(Y|X)}$, why the likelihood is not $p(X,Y|w)$?
From my understanding, according to the Bayes rule $p(B|A)=\frac{p(A|B)p(B)}{p(A)}$. I suppose $A=w$ and $B = X,Y$ in the MAP estimation and get $p(w|X,Y)=\frac{p(X,Y|w)p(w)}{p(X,Y)}$. Even after using the product rule, I could only get $p(w|X,Y)=\frac{p(Y|X,w)p(X|w)p(w)}{p(Y|X)p(X)}$, how to the terms $p(X|w)$ and $p(X)$ cancel out and get the formula above?