I have a circle iwth radius $r$. I want to test the hypothesis that $r \leq 2$ vs. $r >2$ based on the posterior of $r$. $r$ follows the prior distribution: $f(r) = \frac{2}{r^{2}}$, $ r >0.5$. I observed the following points $(x,y): (1,3), (2,1), (0.5,1.4)$. My question is What should be the likelihood?
Edited: The center of the circle is (0,0)