class_docstr: Class for performing sampling in Continuous model
  using No U Turn sampler with dual averaging for
  adaptation of parameter stepsize.
  
  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
  
  delta: float (in between 0 and 1), defaults to 0.65
      The target HMC acceptance probability
  
  Example
  -------
  >>> from pgmpy.sampling import NoUTurnSamplerDA as NUTSda, GradLogPDFGaussian
  >>> from pgmpy.factors.continuous import GaussianDistribution as JGD
  >>> import numpy as np
  >>> mean = np.array([-1, 12, -3])
  >>> covariance = np.array([[-2, 7, 2], [7, 14, 4], [2, 4, -1]])
  >>> model = JGD(['x', 'v', 't'], mean, covariance)
  >>> sampler = NUTSda(model=model, grad_log_pdf=GradLogPDFGaussian)
  >>> samples = sampler.sample(initial_pos=np.array([0, 0, 0]), num_adapt=10, num_samples=10,
  ...                          stepsize=0.25, return_type='recarray')
  >>> samples
  rec.array([(0.0, 0.0, 0.0),
   (0.06100992691638076, -0.17118088764170125, 0.14048470935160887),
   (0.06100992691638076, -0.17118088764170125, 0.14048470935160887),
   (-0.7451883138013118, 1.7975387358691155, 2.3090698721374436),
   (-0.6207457594500309, 1.4611049498441024, 2.5890867012835574),
   (0.24043604780911487, 1.8660976216530618, 3.2508715592645347),
   (0.21509819341468212, 2.157760225367607, 3.5749582768731476),
   (0.20699150582681913, 2.0605044285377305, 3.8588980251618135),
   (0.20699150582681913, 2.0605044285377305, 3.8588980251618135),
   (0.085332419611991, 1.7556171374575567, 4.49985082288814)],
            dtype=[('x', '<f8'), ('v', '<f8'), ('t', '<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 6 : No-U-Turn Sampler with Dual Averaging
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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,
      position0,
      momentum0,
  ):
      """
      Recursively builds a tree for proposing new position and momentum
      """
      if depth == 0:
          (
              position_bar,
              momentum_bar,
              candidate_set_size,
              accept_set_bool,
          ) = self._initialize_tree(
              position, momentum, slice_var, direction * stepsize
          )
  
          alpha = min(
              1,
              self._acceptance_prob(
                  position, position_bar, momentum, momentum_bar
              ),
          )
  
          return (
              position_bar,
              momentum_bar,
              position_bar,
              momentum_bar,
              position_bar,
              candidate_set_size,
              accept_set_bool,
              alpha,
              1,
          )
  
      else:
          (
              position_backward,
              momentum_backward,
              position_forward,
              momentum_forward,
              position_bar,
              candidate_set_size,
              accept_set_bool,
              alpha,
              n_alpha,
          ) = self._build_tree(
              position,
              momentum,
              slice_var,
              direction,
              depth - 1,
              stepsize,
              position0,
              momentum0,
          )
  
          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,
                      alpha2,
                      n_alpha2,
                  ) = self._build_tree(
                      position_backward,
                      momentum_backward,
                      slice_var,
                      direction,
                      depth - 1,
                      stepsize,
                      position0,
                      momentum0,
                  )
              else:
                  # Build tree in forward direction
                  (
                      _,
                      _,
                      position_forward,
                      momentum_forward,
                      position_bar2,
                      candidate_set_size2,
                      accept_set_bool2,
                      alpha2,
                      n_alpha2,
                  ) = self._build_tree(
                      position_forward,
                      momentum_forward,
                      slice_var,
                      direction,
                      depth - 1,
                      stepsize,
                      position0,
                      momentum0,
                  )
  
              if np.random.rand() < candidate_set_size2 / (
                  candidate_set_size2 + candidate_set_size
              ):
                  position_bar = position_bar2
  
              alpha += alpha2
              n_alpha += n_alpha2
              (
                  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,
              alpha,
              n_alpha,
          )
  
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 2 for calling the NoUTurnSamplerDA obj's underlying member method code with example usage: obj._build_tree(position, momentum, slice_var, direction, depth, stepsize, position0, momentum0) and returns: position_bar,  momentum_bar,  position_bar,  momentum_bar,  position_bar,  candidate_set_size,  accept_set_bool,  alpha,  int, position_backward,  momentum_backward,  position_forward,  momentum_forward,  position_bar,  candidate_set_size,  accept_set_bool,  alpha,  n_alpha