Hello,

I’ve been working on this model for a while now and started with a relatively easy model that fitted well as a starting position.

The issues with the model started once I introduced the parameter `t_switch`

as a `vector`

instead of a `real`

and I would be extremely happy if somebody could share some opinion or ideas to help me improve this model.

Besides very long runtimes of up to 60 minutes, my main concern is the high number of divergent transitions which can be between 80 - 90% of the iteration number.

After trying to introduce transformed data and a lot of other things I am at a point where I am running out of ideas because I am still rather inexperienced with Stan.

At the moment my Stan model is fitted to dummy data that is generated on the basis of the same likelihood that Stan has. If useful I can gladly put the code for that in this thread as well. However, as for now here is my stan model:

```
data {
int<lower=0> t;
int N;
vector[t] x;
}
transformed data {
int t_sw_guess;
t_sw_guess = t/N;
}
parameters {
real<lower=0> tau; // characteristic time
vector<lower=0>[N] x2; //for stan N might be enough
vector<lower=0>[N - 1] t_switch; //position of concentration increment
real<lower=0> sigma_x; // fluctuation
}
model {
int m;
real t1;
real t2;
vector[N]t_sw;
// Priors
tau ~ normal(150, 150);
sigma_x ~ exponential(2.5);
for(i in 2:N-1) {
t_switch[i] ~ normal(i*t_sw_guess, t_sw_guess);
}
x2 ~ normal(2, 2);
x[1] ~ normal(x2[1], sigma_x);
m = 1;
t_sw = append_row(t_switch, t);
for (i in 2:t) {
if(m > N) break;
if(i - 1 <= t_sw[m]) {
x[i] ~ normal((x[i - 1] - x2[m]) * exp(-1 / tau) + x2[m], sigma_x * sqrt(1 - exp(-2 / tau)));
} else {
t1 = t_sw[m] - (i - 2);
t2 = (i - 1) - t_sw[m];
x[i] ~ normal(((((x[i - 1]- x2[m]) * exp(-t1 / tau) + x2[m]) - x2[m + 1]) * exp(-t2 / tau)) + x2[m + 1], sigma_x * sqrt(1 - exp(-2 / tau)));
m = m + 1;
}
}
}
```

The model is based on an Ornstein-Uhlenbeck process and will eventually take in data that looks quiet similar to the dummy data as seen in the image here, where the vertical red lines indicate the t_switches.

Letting it run for 3000 iterations in this example (I also tried 5000 and 7000 iterations) I get this pairs plot which indicates a big uncertainty and problem with the `t_switch`

parameters

The last diagnostics I can provide is the nuts_params output in .csv-format

nuts_params.csv (332.7 KB)

I really hope these diagnostics make it easy for someone here with more experience than me to find a mistake or performance weakness in the code.