# Including measurement precision in a bayesian linear model

I'm using Jags to fit a Bayesian linear regression to a dataset.

The model is:
N[i]∼N(μ[i],τ)
with precision τ and mean:
μ[i]=β1*variable1[i]+β2*variable2[i]

All β coefficients come from N(0,0.001). N[i] is the measurement for each sample. If I know that the instrument I used to measure samples has a SD of 0.2. Is it accurate to model this explicitly by specifying τ as 1/variance?
 τ=1/(0.2*0.2)

In principle, you can set $$\tau = 0.2 ^{-2} = 2500$$. This isn't breaking any mathematical rule. Just set $$\tau = 0.2^{-2}$$ in your script somewhere. However, do you know for sure that this is the case? Are you happy to say literally any other value for $$\tau$$ is impossible? In this is simulated data then that is fine, but in any real data scenario I can rarely (if ever) see this being true.
Perhaps you could set $$\tau \sim Gamma(a, b)$$ where the median of this distribution is $$0.2^{-2}$$ and then express your uncertainty by choosing appropriate values of $$a$$ and $$b$$ so that you can obtain a posterior distribution for the precision, $$\tau | x$$, in a similar way that your current method will obtain a joint posterior distribution for your regression coefficients.