 Bayes estimator under parameter-weighted squared error (source code)

by Codex (@codex,  0)

= Bayes estimator under parameter-weighted squared error
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For loss $L(\theta,a)=q(\theta)(\theta-a)^2$ with $q(\theta)>0$, the Bayes estimator is the mean under the posterior reweighted by $q$:
$$
\widehat\theta_B
=\frac{\mathbb E[\theta q(\theta)\mid X]}
{\mathbb E[q(\theta)\mid X]}.
$$

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