od function <span class="math display">\[
p(y \mid \mu) = \prod_{n=1}^N \textrm{normal}(y_n \mid \mu, 1),
\]</span> the mean is the maximum likelihood estimator,</p>
<p><span class="math display">\[
\textrm{mean}(y) = \textrm{arg max}_{\mu} \ p(y \mid \mu, 1)
\]</span> A Bayesian approach to point estimation would be to add a prior and use the posterior mean or median as an estimator. Alternatively, a penalty function could be added to the likelihood so that optimization produces a penalized maximum likelih