class_docstr: Class for performing sampling in Continuous model
  using No U Turn Sampler (a variant of Hamiltonian Monte Carlo)
  
  Parameters
  ----------
  model: An instance pgmpy.models
      Model from which sampling has to be done
  
  grad_log_pdf: A subclass of pgmpy.inference.continuous.GradientLogPDF
      Class to compute the log and gradient log of distribution
  
  simulate_dynamics: A subclass of pgmpy.inference.continuous.BaseSimulateHamiltonianDynamics
      Class to propose future states of position and momentum in time by simulating
      HamiltonianDynamics
  
  Public Methods
  --------------
  sample()
  generate_sample()
  
  Example
  -------
  >>> from pgmpy.sampling import NoUTurnSampler as NUTS, LeapFrog, GradLogPDFGaussian
  >>> from pgmpy.factors.continuous import GaussianDistribution as JGD
  >>> import numpy as np
  >>> mean = np.array([1, 2, 3])
  >>> covariance = np.array([[4, 0.1, 0.2], [0.1, 1, 0.3], [0.2, 0.3, 8]])
  >>> model = JGD(['x', 'y', 'z'], mean, covariance)
  >>> sampler = NUTS(model=model, grad_log_pdf=GradLogPDFGaussian, simulate_dynamics=LeapFrog)
  >>> samples = sampler.sample(initial_pos=np.array([0.1, 0.9, 0.3]), num_samples=20000,
  ...                          stepsize=0.4, return_type='recarray')
  >>> samples
  rec.array([(0.1, 0.9, 0.3),
   (-0.27303886844752756, 0.5028580705249155, 0.2895768065049909),
   (1.7139810571103862, 2.809135711303245, 5.690811523613858), ...,
   (-0.7742669710786649, 2.092867703984895, 6.139480724333439),
   (1.3916152816323692, 1.394952482021687, 3.446906546649354),
   (-0.2726336476939125, 2.6230854954595357, 2.923948403903159)],
            dtype=[('x', '<f8'), ('y', '<f8'), ('z', '<f8')])
  
  References
  ----------
  Matthew D. Hoffman, Andrew Gelman, The No-U-Turn Sampler: Adaptively
  Setting Path Lengths in Hamiltonian Monte Carlo. Journal of
  Machine Learning Research 15 (2014) 1351-1381
  Algorithm 3 : Efficient No-U-Turn Sampler
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docstr: Recursively builds a tree for proposing new position and momentum
docstr_tok: ["Recursively","builds","a","tree","for","proposing","new","position","and","momentum"]
code: def _build_tree(
      self, position, momentum, slice_var, direction, depth, stepsize
  ):
      """
      Recursively builds a tree for proposing new position and momentum
      """
  
      # Parameter names in algorithm (here -> representation in algorithm)
      # position -> theta, momentum -> r, slice_var -> u, direction -> v, depth ->j, stepsize -> epsilon
      # candidate_set_size -> n, accept_set_bool -> s
      if depth == 0:
          # Take single leapfrog step in the given direction (direction * stepsize)
          (
              position_bar,
              momentum_bar,
              candidate_set_size,
              accept_set_bool,
          ) = self._initialize_tree(
              position, momentum, slice_var, direction * stepsize
          )
  
          return (
              position_bar,
              momentum_bar,
              position_bar,
              momentum_bar,
              position_bar,
              candidate_set_size,
              accept_set_bool,
          )
  
      else:
          # Build left and right subtrees
          (
              position_backward,
              momentum_backward,
              position_forward,
              momentum_forward,
              position_bar,
              candidate_set_size,
              accept_set_bool,
          ) = self._build_tree(
              position,
              momentum,
              slice_var,
              direction,
              depth - 1,
              stepsize,
          )
          if accept_set_bool == 1:
              if direction == -1:
                  # Build tree in backward direction
                  (
                      position_backward,
                      momentum_backward,
                      _,
                      _,
                      position_bar2,
                      candidate_set_size2,
                      accept_set_bool2,
                  ) = self._build_tree(
                      position_backward,
                      momentum_backward,
                      slice_var,
                      direction,
                      depth - 1,
                      stepsize,
                  )
              else:
                  # Build tree in forward direction
                  (
                      _,
                      _,
                      position_forward,
                      momentum_forward,
                      position_bar2,
                      candidate_set_size2,
                      accept_set_bool2,
                  ) = self._build_tree(
                      position_forward,
                      momentum_forward,
                      slice_var,
                      direction,
                      depth - 1,
                      stepsize,
                  )
  
              if np.random.rand() < candidate_set_size2 / (
                  candidate_set_size2 + candidate_set_size
              ):
                  position_bar = position_bar2
  
              (
                  accept_set_bool,
                  candidate_set_size,
              ) = self._update_acceptance_criteria(
                  position_forward,
                  position_backward,
                  momentum_forward,
                  momentum_backward,
                  accept_set_bool2,
                  candidate_set_size,
                  candidate_set_size2,
              )
  
          return (
              position_backward,
              momentum_backward,
              position_forward,
              momentum_forward,
              position_bar,
              candidate_set_size,
              accept_set_bool,
          )
  
file_path: pgmpy/pgmpy/sampling/NUTS.py
imports: import numpy
  from tqdm.auto import tqdm
  from pgmpy.sampling import HamiltonianMCDA, LeapFrog, _return_samples
  from pgmpy.utils import _check_1d_array_object, _check_length_equal
label_desc: Use image node_id 4 for calling the NoUTurnSampler obj's underlying member method code with example usage: obj._build_tree(position, momentum, slice_var, direction, depth, stepsize) and returns: position_bar,  momentum_bar,  position_bar,  momentum_bar,  position_bar,  candidate_set_size,  accept_set_bool, position_backward,  momentum_backward,  position_forward,  momentum_forward,  position_bar,  candidate_set_size,  accept_set_bool