Dear Stan comunity,

I’m still new to Stan, and I’ve been facing some problems while writing my code.

I am trying to estimate four parameters, namely C_1, C_2, C_3 and C_4. They are the coefficients of 3rd degree function f(x) = C_1 x^3 + C_2 x^2 + C_3 x + C_4. The only prior information I have about the coefficients is C_4 > 0. Additionally, I know that f(x) > 0 in the range d_{\text{min}} < x < d_{\text{max}}. These values d_{\text{min}} and d_{\text{max}} represent, respectively, the minimum and maximum values of my data. In my problem, x is always between d_{\text{min}} and d_{\text{max}}, so I don’t have to worry about what happens outside this interval.

So far my code is similar to this:

```
functions {
real f(real x, real C_1, real C_2, real C_3, real C_4) {
real my_f = C_1 * pow(x, 3) + C_2 * pow(x, 2) + C_3 * x + C_4;
return my_f;
}
vector complicated_function(C_1, C_2, C_3, C_4) {
real x;
// Do some calculation to find "x", which is a function of C_1, C_2, C_3 and C_4
real y = f(x, C_1, C_2, C_3, C_4);
real z;
// Do some calculation to find "z", which is a function of "y".
return z;
}
}
data {
int n;
vector[n] d;
}
transformed data {
real d_min = min(d);
real d_max = max(d);
}
parameters {
real C1;
real C2;
real C3;
real<lower=0> C4;
}
transformed parameters {
vector[n] ff = complicated_function(C_1, C_2, C_3, C_4);
}
model {
d ~ normal(ff, 1); // Just an example.
}
```

I got stuck when I tried to implement the constraint C_1 x^3 + C_2 x^2 + C_3 x + C_4 > 0 for d_{\text{min}} < x < d_{\text{max}}. I have the impression that I should combine the blocks “transformed data” and “transformed parameters”, but I am not sure how. I would really appreciate if someone could help me with this.

Thanks in advance.

Best regards,

Rodrigo