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I get that the posterior ##p(\theta|y) \propto p(y|\theta)p(\theta)## should be normalized by ##\frac{1}{p(y)}## for the probability to sum to 1, but what about the mean and variance?

Am I not right understanding that sampling from the un-normalized posterior gives the same mean and variance as sampling from the normalized posterior?

Can I prove it mathematically?

Can't find it and can't figure it out.

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# Sampling from normalized and un-normalized posterior

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