Why is the paramter for MAP equal to bayes

I am reading about bayes estimator and it says that the parameter for MAP (maximum a posteriori) estimation is equal to Bayes estimation. However, there is no proof whatsoever and I cannot seem to find proof of this online.

• The author is not actually deriving the MAP estimator here, just writing down a posterior. This appears just to be some algebra, but the author is writing in a very confusing way, using notation that he hasn't even defined yet. Try substituting $\sigma_n^{2} = \left ( 1 / \sigma^2_0 + n / \sigma^2 \right )^{-1}$ into (17) and see if you get (16). Oct 10, 2016 at 14:28