I was going through maximum a posteriori estimation and could not understand, why argmax is used for first term in image shown below but missing from second term. Shouldn't we have used argmax for both of them? If not what is the reasoning behind this.
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You are misreading the notation.
$$ \underset{\theta}{\operatorname{arg\,max}} \log P(X|\theta) + \log P(\theta) = \underset{\theta}{\operatorname{arg\,max}} \Big( \log P(X|\theta) + \log P(\theta) \Big) $$
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$\begingroup$ Thanks, now you cleared my confusion. So I can add bracket before all equation down the line and before summation, without changing the meaning. Obviously p(theta) is constant, so need of argmax. $\endgroup$ Commented Oct 15, 2021 at 14:20