# Alternatives to MAP estimator

Given some data $y$, dependent on parameter $\theta$, I have some density $p(\theta | y)$. I now want to infer what value of $\theta$ is most `likely' to have originated $y$. One possibility of doing this is calculating the MAP estimate of $\theta$. However, I was wondering if there are other ways of finding candidates for $\theta$, preferably in a Bayesian setting?

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The mean of the posterior sample, the median ... For a discussion of Bayesian estimation see. –  user10525 Jul 31 '12 at 14:18
Yes I agree with procrastinator. Bayesians believe that the posterior distribution characterizes our current knowledge of theta and so if you want a point estimate you have many choices, mean, median and mode have already been mentioned. A from of trimmed mean might be another possibility. In the frequency setting there is method of moments and maximum likelihood. Perhaps the shape of the a posteriori distribution could dictate the choice much like frequentists choose based on what best represents the center of the distribution. –  Michael Chernick Jul 31 '12 at 15:19