I have been looking at this explanation of writing a posterior in terms of likelihood and prior can any one please explain the detailed steps to go from one line to the next? I started to believe that there is something wrong
this is coming from slide 23 in this lecture http://www.columbia.edu/~jwp2128/Teaching/W4721/Spring2017/slides/lecture_1-26-17.pdf
First, by the fact $p(A, B \mid C) = p(A \mid B, C)\cdot p(B\mid C)$, we have $$ p(w \mid y, X) = \frac{p(y \mid w, X) p(w \mid X)}{p(y \mid X)} \tag{$1$} $$ Next, since $w$ is independent of $X$, we have $$ p(w \mid X) = p(w) \tag{$2$} $$ Combining $(1)$ and $(2)$, you can get the second line.