In the paper here, just before equation 12, authors introduce likelihood function $\pi(r|\theta)$. What does $\theta$ represent here ?. What is the intuitive explanation behind equation 12?
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To me, it looks like $\theta$ is just a throw-away "any variable". They might just as well have written $r(s|\cdot)$.
Equation 12 is just saying that because $r$ and $s$ are mutually independent, the distribution of the error $\rm\bf e$ does not change. Compare (12) with (10) rearranged to give an expression for $\rm\bf e$.
Peter K.
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The $\theta$ seems to come out of no where. It was never mentioned before or after. – Sajil C K Sep 19 '17 at 01:20
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@SajilC.K. : Yes, $\theta$ is often used as the general "parameter vector". As I say, it's just a throw-away remark. – Peter K. Sep 19 '17 at 01:29