Defining discrete uniform parameter

Modeling
,
1

Hi all. Am trying to code a simple hierarchical model in Stan as an exercise.

Y \sim Pois(10kt); t \sim Exp(2/k); k \sim Unif\{1,2,3\}

I was trying to use discrete_range() for the discrete uniform distribution for k on the set {1,2,3}. First, it will not accept k as integer parameter so I used real. Then in the model section it will not recognize discrete_range() with or without suffixes _lpmf, etc. How can I code this- Should I be using some other function besides discrete_range? Thanks
Mike

data {
  int<lower=0> N;
   int<lower = 0> y;    // 
}
parameters {
  real<lower = 1> k;   // Did not like int.
  real<lower=0> t;
}

model {
  y ~ poisson(10*k*t);  
  t ~ exponential(2/k);
  k ~ discrete_range(1,3);  \\ Will not accept discrete_range, or discrete_range_lpmf, etc. 
}
2

Stan does not support discrete parameters, but the parameter k can be marginalized out of this model. Since this is an exercise I’ll refrain from providing the marginalized solution, but I’m happy to help more if you get stuck!

3

Okay thanks! In fact I did this marginalization by hand/numerically for k and t but was trying to reproduce. I suppose since you can always do this it does not make sense simulate/approximate the posterior.