code: def log_grow_ratio(
      combined_node: LeafNode,
      left_node: LeafNode,
      right_node: LeafNode,
      sigma: Sigma,
      sigma_mu: float,
  ):
      # deviation: https: // www.cs.ubc.ca / ~murphyk / Papers / bayesGauss.pdf
      var = np.power(sigma.current_value(), 2)
      var_mu = np.power(sigma_mu, 2)
      n = combined_node.data.X.n_obsv
      n_l = left_node.data.X.n_obsv
      n_r = right_node.data.X.n_obsv
  
      # first_term = (var * (var + n * sigma_mu)) / ((var + n_l * var_mu) * (var + n_r * var_mu))
      # first_term = np.log(np.sqrt(first_term))
  
      combined_y_sum = combined_node.data.y.summed_y()
      left_y_sum = left_node.data.y.summed_y()
      right_y_sum = right_node.data.y.summed_y()
  
      left_resp_contribution = np.square(left_y_sum) / (
          var + n_l * sigma_mu
      )
      right_resp_contribution = np.square(right_y_sum) / (
          var + n_r * sigma_mu
      )
      combined_resp_contribution = np.square(combined_y_sum) / (
          var + n * sigma_mu
      )
  
      # resp_contribution = left_resp_contribution + right_resp_contribution - combined_resp_contribution
  
      numerator_first = np.log(
          np.sqrt(((var + n_l * var_mu) * (var + n_r * var_mu)))
      )
      numerator_second = (var_mu / (2 * var)) * (
          left_resp_contribution + right_resp_contribution
      )
  
      big_model_l = numerator_first + numerator_second
  
      denominator_first = np.log(np.sqrt((var * (var + n * var_mu))))
      denominator_second = (
          var_mu / (2 * var)
      ) * combined_resp_contribution
  
      small_model_l = denominator_first + denominator_second
  
      return big_model_l, small_model_l
  
imports: from typing import List
  import numpy
  from ...model import Model
  from ...mutation import TreeMutation, GrowMutation, PruneMutation
  from ...node import LeafNode, TreeNode
  from ...samplers.treemutation import TreeMutationLikelihoodRatio
  from ...sigma import Sigma
  from ...tree import Tree
label_desc: Use image node_id 1 for calling a global function with example usage: log_grow_ratio(combined_node, left_node, right_node, sigma, sigma_mu) and returns: big_model_l,  small_model_l