And I'd probably make the noise term multiplicative and non-negative, instead of additive, to prevent the sampler from landing on a negative sales figure, which is presumably nonsensical in this context.
I know JAGS lets you put interval limits onto terms which lets you specify that some variable must be non-negative (looks something like dist(x,y)[0,∞]), so maybe STAN has something similar.
It does. However...
I see now I could've described the model better. In Stan I don't think you can literally write the observed data as the sum of the signal and the noise; I think the data always has to be incorporated into the model as something sampled from a probability distribution, so you'd actually translate the simplest additive model into Stan-speak as something like
data {
int<lower=1> N;
int<lower=1> Ncities;
int<lower=1> Nwidgets;
int<lower=1> city[N];
int<lower=1> widget[N];
real<lower=0&
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