code: def test_ModelListGP(self) -> None:
      for dtype, outcome_transform in itertools.product(
          (torch.float, torch.double),
          ("None", "Standardize", "Log", "Chained"),
      ):
          model = self._base_test_ModelListGP(
              fixed_noise=False,
              dtype=dtype,
              outcome_transform=outcome_transform,
          )
          tkwargs = {"device": self.device, "dtype": dtype}
  
          # test observation_noise
          test_x = torch.tensor([[0.25], [0.75]], **tkwargs)
          posterior = model.posterior(test_x, observation_noise=True)
  
          gpytorch_posterior_expected = outcome_transform in (
              "None",
              "Standardize",
          )
          expected_type = (
              GPyTorchPosterior
              if gpytorch_posterior_expected
              else PosteriorList
          )
          self.assertIsInstance(posterior, expected_type)
          if gpytorch_posterior_expected:
              self.assertIsInstance(
                  posterior.distribution, MultitaskMultivariateNormal
              )
          else:
              self.assertIsInstance(
                  posterior.posteriors[0], TransformedPosterior
              )
  
          # Test tensor valued observation noise.
          observation_noise = torch.rand(2, 2, **tkwargs)
          with torch.no_grad():
              noise_free_variance = model.posterior(test_x).variance
              noisy_variance = model.posterior(
                  test_x, observation_noise=observation_noise
              ).variance
          self.assertEqual(
              noise_free_variance.shape, noisy_variance.shape
          )
          if outcome_transform == "None":
              self.assertAllClose(
                  noise_free_variance + observation_noise,
                  noisy_variance,
              )
  
imports: import itertools
  import warnings
  from copy import deepcopy
  from typing import Optional
  import torch
  from botorch.acquisition.objective import ScalarizedPosteriorTransform
  from botorch.exceptions.errors import BotorchTensorDimensionError
  from botorch.exceptions.warnings import OptimizationWarning
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.multitask import MultiTaskGP
  from botorch.models.transforms.input import Normalize
  from botorch.models.transforms.outcome import ChainedOutcomeTransform, Log, Standardize
  from botorch.posteriors import GPyTorchPosterior, PosteriorList, TransformedPosterior
  from botorch.sampling.base import MCSampler
  from botorch.sampling.list_sampler import ListSampler
  from botorch.sampling.normal import IIDNormalSampler
  from botorch.utils.testing import _get_random_data, BotorchTestCase
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from gpytorch.kernels import MaternKernel, ScaleKernel
  from gpytorch.likelihoods import LikelihoodList
  from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood, GaussianLikelihood
  from gpytorch.means import ConstantMean
  from gpytorch.mlls import SumMarginalLogLikelihood
  from gpytorch.mlls.exact_marginal_log_likelihood import ExactMarginalLogLikelihood
  from gpytorch.priors import GammaPrior
  from torch import Tensor
label_desc: Use image node_id 2 for calling the TestModelListGP obj's underlying member method code with example usage: obj.test_ModelListGP() without return types