When discussing sigmoids at Dose Response Model with partial pooling on maximum value I’ve found a parametrization that I am quite happy about, but it requires three parameters a,b,c that satisfy somewhat weird conditions:

The best way I can implement this is:

```
parameters {
real<lower=0> a;
real<lower=0> c;
real<lower=sqrt(a * c), upper=max({a,c})> b;
}
```

(note that the inequality \min{\{a,c\}} < b is implied by the constraints used).

The model works neatly if I enforce the order of a and c by a constraint, or if the data are informative enough to force the ordering (a,b,c here are basically directly observable in data). I suspect (though am not sure) that the main problems I have remaining are related to the non-smoothness from the `max({a,c})`

when the ordering of a and c changes.

Without the b^2 > ac condition, this could be a straightforward extension of the lower and upper bounded scalar constraint, but I can’t figure out how to enforce the additional limitation.

Thanks for any ideas.