= Solution
Delete the plate <random effects> from the <linear predictor> and remove their stochastic nodes and the unused scale/precision nodes. The observation layer then remains a <Poisson distribution> with
$$
\boxed{\log\mu_{ij}=\alpha+\beta\log(x_i+10)+\gamma x_i.}
$$
For example the essential <WinBUGS> observation block can be written as
``
for (i in 1:doses) {
for (j in 1:plates) {
y[i,j] ~ dpois(mu[i,j])
log(mu[i,j]) <- alpha + beta*log(x[i]+10) + gamma*x[i]
}
}
``
Retain the coefficient priors. This is the $\tau=0$ sampling model implemented directly; attempting to keep `1/(tau*tau)` while fixing `tau` to zero would divide by zero.
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