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 Quote by kasraa Part one: The posterior $$p \left( x|Z \right)$$, has a mean and a (co)variance. Its mean is the MMSE estimator, $$E \left[ x|Z \right]$$, and its variance (or the trace of its covariance matrix, if it's a random vector) is the minimum mean squared error. Am I right? Thanks.
I don't think so. For a random vector of observations, the MMSE for the posterior estimate is the minimized trace of the covariance matrix. This is consistent with the discussion in the link I provided. As for the rest, I'm not following you. I don't understand why you're double conditioning on Z for instance. Someone else will have to try and help you