# Power of Uniform Distribution?

In the Bayesian analysis, $\mathtt{rjags}$ in particular, it is very frequent to see the code:

sigma ~ dunif(0, 100)
sigma.1 <- pow(sigma, -2)


But, what does this mean? Is this meaning that $\sigma\sim Unif(0.01, 100)$ and $\sigma_1=\sigma^{-2}$ and we are doing a transformation of the uniform distribution? As I do the transformation, I got the pdf of $\sigma_1$ to be $\frac{y}{50}$ over $(100^{-2}, +\infty)$, which indeed is not a valid density if I did not make any mistake in my calculations.

Any explanations? Thanks!

• Can you give a link to such a code ? – peuhp Apr 29 '16 at 14:50
• @peuhp biostat.umn.edu/~brad/data/dugongsNL_BUGS.txt Here is an example. See the model part. – user132565 Apr 29 '16 at 14:51
• You got confused in the change of variable, the Jacobian returns $\sigma_1^{-3/2}$. – Xi'an Apr 29 '16 at 14:51

dnorm(location,precision)

where precision is the precision i.e. by definition $1/\sigma^2$ and generally denoted as $\tau$. So the prior on $\sigma$ is uniform (which has its limits but it is another question see e.g. Weakly informative prior distributions for scale parameters)