From this article:
"...a maximum-a-posteriori $(MAP_{x,k}^{\,\,\,\,\,1})$ estimation, seeking a pair $(\hat{x}, \hat{k})$ maximizing: $$p(x, k\mid y) \propto p(y|x, k)p(x)p(k).$$
Are $\hat{x}$ and $\hat{k}$ the normalized version of vectors $x$ and $k$, having length $1$? If so, could someone explain me why this does make sense?