A maximum a posteriori (MAP) estimation maximizes the posterior distribution using Bayes' rule and provides a point estimate. Is it correct to say that MAP is a Bayesian inference method? Or does 'Bayesian inference' only refer to methods that estimate the full posterior distribution (as opposed to a point estimate)?
$\begingroup$ Why wouldn't it? $\endgroup$– Tim ♦Feb 17, 2018 at 12:39
$\begingroup$ From what I have seen, some consider that the term 'Bayesian inference' or 'Bayesian estimation' is reserved for methods that estimate the full posterior distribution, and classify MAP (and maximum likelihood) estimations as other methods because they provide point estimates. Others seem to consider that MAP can be considered as 'Bayesian inference' because it provides the mode of the posterior distribution. So it's a bit confusing for me, and would like to make sure to use the correct terminology (if there is one...) $\endgroup$– EphFeb 17, 2018 at 13:06
1$\begingroup$ This question has already been asked on this forum. Several times.. There are many arguments against MAP being Bayes estimates, one being the dependence on the dominating measure. $\endgroup$– Xi'anFeb 17, 2018 at 14:07