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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)

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1 Answer 1

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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.

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  • $\begingroup$ In this case, the SD of the measurement is calculated for the instrument and so is a discrete value. But I hear what you are saying. Is there a way to set the median for a gamma distribution? Perhaps I could just set the SD as coming from dnorm(0.2,0.001) to allow that uncertainty and pull τ from that. $\endgroup$
    – Sovay
    Jun 17, 2020 at 19:24
  • $\begingroup$ You should set the sd (or variance or precision) to be strictly positive. You could instead set log(sd)~normal( log(0.2), v) where v is chosen to represent your uncertainty about the sd appropriately. $\endgroup$
    – jcken
    Jun 17, 2020 at 20:26

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