Hi all, I’m trying to get familiar with Stan, but have difficulties building a model. I looked in different topics and documentations but couldn’t find a template, which fits my needs.

What I want to do: I have a dynamic system, consisting of ca. 200 differential equations, containing 50 parameters I need to sample. The measure for the data is a constellation of some states at different timepoints for 10 different initial states. I hope I can explain it with an example: I know in the experiment with initial state [1,2,1,1,3,4,…,1] that at t=50s I measured x[4]+x[79]+x[97]+x[179]=153. There is no way to measure the states separately. I know from the nature of the experiment that my measure is normal distributed, where the sigma and the scale is unknown. So it would be great to have also a sampling for sigma and scale.

I tried to build the model, but can’t figure out, how to implement the data. Here is my attempt with a smaller artificial model.

```
functions {
real[] reactions(real t,
real[] x,
real[] theta) {
real dxdt[10];
dxdt[1] = theta[1]*x[2] - theta[2]*x[1];
dxdt[2] = - theta[3]*x[2];
dxdt[3] = theta[4]*x[4]*x[4] - theta[5]*x[1];
dxdt[4] = - theta[2]*x[4];
dxdt[5] = theta[4]*x[5] - theta[6]*x[2];
dxdt[6] = - theta[1]*x[8];
dxdt[7] = theta[3]*x[6] - theta[6]*x[2];
dxdt[8] = theta[5]*x[10];
dxdt[9] = theta[3]*x[8] + theta[2]*x[9];
dxdt[10] = theta[6]*x[9];
return dxdt;
}
}
data {
int<lower=1> T;
int<lower=1> C;
real<lower=0> measure[T,C,3];
real initial[C,10]
real ts[T];
}
parameters {
vector<lower=0>[8] sigma;
real<lower=-5,upper=5> theta[6];
}
transformed parameters {
real x_hat[T,2];
for(c in 1:C)
x_hat[c] = integrate_ode_bdf(reactions, initial[c], 0, ts, theta);
}
model{
sigma~cauchy(0,1);
for (t in 1:T)
for(c in 1:C)
measure[t,c,1]~normal(x_hat[c,2]+x_hat[c,5]+x_hat[c,6],sigma);
measure[t,c,2]~normal(x_hat[c,1]+x_hat[c,4]+x_hat[c,6],sigma);
measure[t,c,3]~normal(x_hat[c,4]+x_hat[c,7],sigma);
}
```

Obviously this doesn’t work at all, but I would be happy for any help you can provide. This doesn’t help me: http://mc-stan.org/events/stancon2017-notebooks/stancon2017-margossian-gillespie-ode.html .