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In my class notes both MPE (Minimum Probability of Error) and MAP (Maximum Aposteriori Probability) estimators are shown as:

$$h_{MPE}(\mathbf x) = posterior\ mode = arg\ max_{y\in Y}p(y|\mathbf x)$$ $$h_{MAP}(\mathbf x) = posterior\ mode = arg\ max_{y\in Y}p(y|\mathbf x)$$

So what's the difference between these? Do you just follow this same formula to determine either the MPE or MAP estimate?

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    There clearly isn't any difference between the two formulas that you've given. Either you made an error in your note taking or there's some missing context that might explain why the author wants to use these two names. – 2017-02-15
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    I know that the formulas are the same, but since there are two different terms for the same formula I'm wondering why this is and in what context this makes a difference. That's exactly what my question is. – 2017-02-15

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