Shouldn't use MAP terminology in Bayes risk context (Concept Check 1)

[davidrosenberg]

Although mathematically finding a MAP estimate involves finding the argmax of a probability mass function (or density function), and that's exactly what we're doing here, I think that terminology is specific to the Bayesian framework.

https://github.com/davidrosenberg/mlcourse/blob/gh-pages/ConceptChecks/1-Lec-Check_sol.pdfhttps://github.com/davidrosenberg/mlcourse/blob/gh-pages/ConceptChecks/1-Lec-Check_sol.pdf

[davidrosenberg]

On further reflection... maybe this is fine: say you have a classic latent variable model z --> x, where x is observed, z is latent. When the distributions of z and x are parameterized by a parameter theta, it makes sense to talk about a MAP estimate of theta (in bayesian context) or ML estimate of theta (frequentist context). But I think it would confusing to also talk about the MAP of z.

However, with parameter theta fixed, we have a full joint distribution over z and x, with x observed and z unobserved --- mathematically that's exactly the Bayesian setting. So if there are no parameter to estimate, then it pretty clear what's meant...