Yes, I am happy to share my code. I considered this for hours. The only reason I am not to do this is that it may be an impolite behavior that shares Stan code in PyMC3 community.
Here is my code:
data {
int<lower=0> N; // trial number
int y[N];
}
parameters {
real k;
real<lower=0.1, upper=0.9> r[N];
real v[N];
}
model {
k~uniform(-10,10);
for(t in 1:N){
if(t == 1){
v[t] ~ uniform(0,100);
r[t] ~ normal(0.5,0.3);
}
else{
v[t] ~ normal(v[t-1],exp(k));
r[t] ~ beta_proportion(r[t-1],exp(v[t]));
}
y[t] ~ bernoulli(r[t]);
}
}