Changing a conditional probability to a deterministic function

by KRL   Last Updated June 20, 2019 02:19 AM

Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this conditional density as a deterministic function of $x$ and $\theta$ where $\theta$ is a random variable independent of $x$? Furthermore, is this representation unique?

For example, if $y$ has a Gaussian distribution with mean $x$ and s.d. $\sigma^*$, we can write

$y = x + \sigma,$

where $\sigma$ has a Gaussian distribution with mean zero and s.d. $\sigma$. My question might be related to the question discussed here.



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