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"...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?

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This is related to statistics, and $(\hat{x}, \hat{k})$ are not normalized-things but estimators, found by optimizing a given function. See here: en.wikipedia.org/wiki/Maximum_a_posteriori_estimation –  Jean-Claude Arbaut Mar 13 '13 at 11:28
    
If $x$ is the observation variable then $\hat{x}$ denotes the predicted (or fitted) value. –  Stéphane Laurent Mar 13 '13 at 11:49
    
Why do we write bayes's rule in this form and not like this: $P(A_n|B) \propto P(B|A_n) P(A_n) $ –  user1095340 Mar 20 '13 at 7:18
    
arbautjc @Stéphane-Laurant: Which books would you recommend to learn more? –  user1095340 Apr 1 '13 at 17:15
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