docs: def _init_ws(n_items, comparisons, prior_inv, tau, nu):
      """Initialize parameters in the weight space."""
      prec = np.zeros((n_items, n_items))
      xs = np.zeros(n_items)
      for i, (a, b) in enumerate(comparisons):
          prec[(a, a, b, b), (a, b, a, b)] += tau[i] * MAT_ONE_FLAT 
          xs[a] += nu[i]
          xs[b] -= nu[i]
      cov = inv_posdef(prior_inv + prec)
      mean = cov.dot(xs)
      return mean, cov, xs , prec