Test: Soft vs Hard sum-to-zero constrain + choosing the right prior for soft constrain

Modeling
32

Trying to use this right know :-) - Thanx for the effort and sharing. If I understand it correctly, the code should be used as:

transformed data {
  vector[2*N] Q_r = Q_sum_to_zero_QR(N);
  real x_raw_sigma = inv_sqrt(1 - inv(N));
}

parameters {
   vector[N - 1]  x_raw;
}

transformed parameters {
  vector[N] x = sum_to_zero_QR(x_raw, Q_r);
}

model {
  x_raw ~ normal(0, x_raw_sigma);
}

where the non-obvious fact is that x_{raw} \sim N \left( 0, \frac{1}{\sqrt{1 - \frac{1}{N}}} \right)

3 Likes