# Hierarchical Bayesian model - issues with JAGS/BUGS switching between lognormal and normal

I'm trying to construct a hierarchical model using JAGS, but I'm running into issues converting between normal/lognormal distributions and the more I stare at my problem, the more confused I get.

Some of the parameters I'm trying to estimate are a series of $M$ values - I know that $M$ is lognormally distributed. In order to estimate the mean of $M$ (the hierarchy), I want to use the normal distribution because I have prior information that the mean is likely around $0.2$.

I know that the following equations hold for when you 'switch' between inputting your values from a normal distribution (let's call it $X$) and a lognormal ($Y$, where $Y=\ln(X)$):

$\mu_Y = \ln(\mu_X) - 0.5\ln(1 + \frac{\sigma_X^2}{\mu^2_X}) = \ln (\mu_X) -0.5\sigma_Y^2$

$\sigma_Y^2 = \ln(1 + \frac{\sigma_X^2}{\mu^2_X})$

However, I'm having issues implementing these in my JAGS model code. Here's the relevant piece of code:

meanM ~ dnorm(0.2, 0.1)
precM ~ dgamma(0.001, 0.001)
varM <- 1 / precM
logvarM <- log(1 + (varM / (meanM * meanM)))
logprecM <- 1 / logvarM
logmeanM <- log(meanM) - (0.5 * logvarM)

for (k in 1:4){
M[k] ~ dlnorm(logmeanM, logprecM)
}


I get an error from JAGS here that says that logmeanM has an invalid parent value, and when I try to debug it using OpenBUGS it says that something went wrong in procedure Ln in module Math. Am I completely wrong in my math or my code? The more I try to figure it out, the more confused about normal/lognormal I get, so apologies if that is reflected in this question.

meanM is apparently intended to be the mean of a lognormal random variable. The mean of a lognormal distribution cannot be negative. Therefore, you cannot put a normal prior on meanM since a normal distribution puts positive probability on negative values.
• I thought of that, but I tried setting up something like meanM ~ dnorm(5, 10), which has little probability of having a negative value, and I still got the same error. – Peter Apr 22 '16 at 19:28