Dinamic prior based on categorical information

Modeling
,
1

Hello everyone,

I’m new to Stan, and looking at the blog or documentation, I haven’t found the answer to my question.

I would like to have a simple linear model with one independent variable. I can’t measure exactly the independent variable values, but I can put them in bins and I can estimate a rough distribution for these bins.

What is the best way to do that in stan?

I was thinking at something like:

data {
  int N;
  vector[N] dependent_oserved;
  vector[N] independent_cat;
}
parameters {
  real<lower=0> b0;
  real b1;
  vector<lower=0, upper=1>[N] independent;
  vector[N] dependent;
}
model {
  b0 ~ normal(0,10);
  b1 ~ normal(0,10);
  for (i in 1:N) {
    	  if (independent_cat[i] == 'factor_1') {
          independent[i] ~ normal(1,0.45);
    	  }
        if (independent_cat[i] == 'factor_2') {
          independent[i] ~ normal(1,5);
    	  } 
        }
  dependent_oserved ~ normal(dependent,.5);
  dependent ~  normal(b0 + b1*independent, 10);
}"

But how could I implement this in stan? Or is there a better way to approach this problem?

Best regards
Luca