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I was reading this article in wikipedia related to MAP http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation. However, I had this confusion when it says

MAP estimation is a limit of Bayes estimators (under the 0-1 loss function), it is not very representative of Bayesian methods in general.

What does it mean MAP estimation is a limit and it has presented a criticism of MAP stating that the mean/median estimates will be better. I didn't get why it is so? Any guidance will be appreciated.

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    $\begingroup$ This is explained in pp 2 of this document. $\endgroup$
    – user10525
    Commented Dec 26, 2012 at 19:39

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