Find likelihood for a given posterior
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Let $p(z)=mathcal{N}(z|0,1)$ be the standard normal density. Is there a conditional density $p(x|z)$ that could be expressed analytically and that would make the posterior $p(z|x)=mathcal{N}(z|phi(x), bullet)$ a normal distribution whose mean is a non-linear function of $x$ (say, $phi(x)=x^2$ for example) ? The variance could be arbitrary.
probability statistics normal-distribution machine-learning bayesian
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asked Jan 13 at 15:22
Nocturne Nocturne
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