//sporcle.stan

data {
  int<lower=0> N; //Num countries
  int<lower=0> C; //Num continents
  
  real y[N]; //Response
  vector[N] p; //log-Population
  matrix[N,C] X; //Continent
}

parameters {
  //real intercept;
  real beta_population;
  vector[C] beta_continent;
  real<lower=0> sigma;
  real<lower=1> nu;
}

transformed parameters {
  vector[N] theta;
  theta = beta_population * p + X*beta_continent;
}

model{
  nu ~ gamma(2,0.1);
  sigma ~ cauchy(0,3);
  beta_population ~ normal(0,100);
  beta_continent ~ normal(0,100);
  
  y ~ student_t(nu,theta,sigma);
}