Continuous bernoulli

Modeling
#1

@StaffanBetner I was playing around with the continuous bernoulli and if p is a vector I needed to divide the normalizing constant by the sample size.

The stan code. Note that in Stan 2.29 you can declare the same function name with different inputs, one is a vector of p and the other is a real p. Does this seem right?

 real continuous_bernoulli_lpdf(vector y, vector lambda) {
   int N = num_elements(y);
   real lp = N * log2();
   real lp_c = 0;
   int counter = 0;
   
   for (n in 1:N) {
    lp += y[n] * log(lambda[n]) + (1 - y[n]) * log1m(lambda[n]); 
      if (lambda[n] != 0.5) {
        counter += 1;
        lp_c += log( atanh(1 - 2 * lambda[n]) / (1 - 2 * lambda[n]) );
      }
   }
    return lp + lp_c / counter;
 } 
  
  real continuous_bernoulli_lpdf(vector y, real lambda) {
   int N = num_elements(y);
   real lp = N * log2() + sum(y * log(lambda) + (1 - y) * log1m(lambda));
   
    if (lambda != 0.5)
      lp += log( atanh(1 - 2 * lambda) / (1 - 2 * lambda) );
      
    return lp;
 }
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