I am trying to understand Bayesian estimation and I come across this line in my lecture notes:
θ(Bayesian) = E_θ|x[θ] = E[π(θ|x)]
So it's meant to reader that the Bayesian estimator is the Conditional Expectation of the sample (x's) which equals the expectation of the posterior (3'rd expression). I understand the derivation up to this point but I dont see how the conditional expectation of theta:
So the middle expression "E_θ|x[θ]" (should look like E underscore θ|x of θ) is:
Integral [θ · π(θ|x) dθ]
and somehow that equals the expectation of the Posterior i.e.
Please help! I am hoping it is a simple answer cause there is no explanation between these steps.