Section 22.2 of the Stan reference manual mentions that a Jacobian adjustment is not needed when “the transformed parameters are being used rather than given a distribution”. I’m curious how this can be in my specific case where I have something like the following.

```
data {
int<lower=1>n;
int<lower=1>m;
vector<lower=0>[m] dA[n];
vector[m] x[n];
real<lower=0> sigma;
}
parameters {
real<lower=0> A0[n];
vector[m] y;
}
transformed parameters {
vector[m] mu[n];
for (i in 1:n) {
mu[i] = y - log(A0[i] + dA[i]);
}
}
model {
for (i in 1:n) {
x[i] ~ normal(mu[i], sigma);
}
//...priors...
}
```

The above model would appear to need no Jacobian adjustment, and Stan does not raise any message to that effect. It seems to me that an equivalent model would be to swap `x[i]`

with `mu[i]`

in the model block; however in that case this would need a Jacobian adjustment. In both cases the pdf is the same (since it’s symmetric for x and mu), so how to understand this difference?