code: def _check_posterior_type(
      posterior: Posterior,
  ) -> Union[GPyTorchPosterior, PosteriorList]:
      """Check whether the posterior type is  `GPyTorchPosterior` or `PosteriorList`."""
      if isinstance(posterior, GPyTorchPosterior) or isinstance(
          posterior, PosteriorList
      ):
          return posterior
      else:
          raise ValueError(
              f"Value was not of type GPyTorchPosterior or PosteriorList:\n{posterior}"
          )
  
imports: from __future__ import annotations
  from typing import Callable, cast, Dict, List, Optional, Tuple, Union
  import torch
  from ax.exceptions.core import AxError
  from ax.models.torch.botorch_defaults import NO_FEASIBLE_POINTS_MESSAGE
  from ax.models.torch.utils import _get_X_pending_and_observed, get_outcome_constraint_transforms, subset_model
  from ax.models.torch_base import TorchModel
  from ax.utils.common.typeutils import checked_cast, not_none
  from botorch.acquisition import get_acquisition_function
  from botorch.acquisition.acquisition import AcquisitionFunction
  from botorch.acquisition.multi_objective.logei import qLogExpectedHypervolumeImprovement, qLogNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.multi_objective.monte_carlo import qExpectedHypervolumeImprovement, qNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.multi_objective.objective import WeightedMCMultiOutputObjective
  from botorch.acquisition.multi_objective.utils import get_default_partitioning_alpha
  from botorch.models.model import Model
  from botorch.optim.optimize import optimize_acqf_list
  from botorch.posteriors.gpytorch import GPyTorchPosterior
  from botorch.posteriors.posterior import Posterior
  from botorch.posteriors.posterior_list import PosteriorList
  from botorch.utils.multi_objective.hypervolume import infer_reference_point
  from botorch.utils.multi_objective.pareto import is_non_dominated
  from torch import Tensor
label_desc: Use image node_id 12 for calling a global function with example usage: _check_posterior_type(posterior) and returns: posterior