I’m working on a model with fairly many parameters (>5000) and is approaching 1000 lines of code, so I won’t attempt to get input on the entire thing, but I believe I have found some candidate parameters that might be causing my current problems with divergence, plotted as pairs below. The analysis is temporal, and each time `iy`

has a parameter `u[t]`

, which is the autocorrelated temporal effect on “the thing this is modeling.” There are currently 11 time steps (NrOfYears) in the model.

`logSu`

is the logarithm of standard deviation, `Su`

, of `u`

`logit_rhou`

is the logit-transform of first order autocorrelation `rhou`

(I have for now excluded negative AC)

`umean`

is the average parameter that u are distributed around

`u_raw[1]`

,`u_raw[2]`

are examples the transformed parameters `u`

on which they are updated.

I’m pasting in the code involving these parameters below in the hope that it might be sufficient to understand how they are modeled. One apparent issue is the funnel behavior `umean`

. If that occur for the effects `x`

around the mean, it often works to `x[i]=x_raw[i] * sigma`

and `x_raw[i] ~ normal(0, 1)`

, but here it’s the mean that has a funnel behavior. Any idea of how to transform `meanu`

to escape the funnel? I also think the correlation between `logSu`

and `logit_rhou could be problematic.

In the plot, the blob of red dots are all from the same chain where almost all iterations diverged.

Grateful for any input.

Transformed parameters

```
rhou=inv_logit(logit_rhou);
Su=exp(logSu);
for (iy in 1:NrOfYears){
if (iy == 1){
u[iy]=u_raw[iy] * Su;
}else{
u[iy] = rhou*u[iy-1] + u_raw[iy] * sqrt(1-rhou^2) *Su;
}
}
for (il in 1:NrOfLans){
for (iy in 1:NrOfYears){
loga[il,iy] = umean + u[iy]+v[il]; //the part of the model involving v appears to behave better
a[il,iy] = exp (loga[il,iy] );
}
}
```

Model

```
rhou~beta(1,1);
target += log_inv_logit(logit_rhou) + log1m_inv_logit(logit_rhou);
for (iy in 1:NrOfYears){
u_raw[iy] ~ normal(0, 1);
//
}
Su ~ cauchy(0,2.5);
target += logSu;
```