This question is influenced by this: Help in understanding Derivation of Posterior in Gaussian Process .
The question is
1) What would happen if our posterior had this form: $p(w|X,y)= \frac{1}{D}p(y|X,w)p(w)$. Notice that $\frac{1}{D}$ is some constant, how do we deal with such a thing?
2) I noticed that in gaussian process book, they use a prior with $\mu=$ $0$. What if it was something like this: $p(w)=\mathcal{N}(w_{0},\Sigma)$. ?