code: def _base_test_ModelListGP(
      self, fixed_noise: bool, dtype, outcome_transform: str
  ) -> ModelListGP:
      tkwargs = {"device": self.device, "dtype": dtype}
      model = _get_model(
          fixed_noise=fixed_noise,
          outcome_transform=outcome_transform,
          **tkwargs,
      )
      self.assertIsInstance(model, ModelListGP)
      self.assertIsInstance(model.likelihood, LikelihoodList)
      self.assertEqual(model.num_outputs, 2)
      for m in model.models:
          self.assertIsInstance(m.mean_module, ConstantMean)
          self.assertIsInstance(m.covar_module, ScaleKernel)
          matern_kernel = m.covar_module.base_kernel
          self.assertIsInstance(matern_kernel, MaternKernel)
          self.assertIsInstance(
              matern_kernel.lengthscale_prior, GammaPrior
          )
          if outcome_transform != "None":
              self.assertIsInstance(
                  m.outcome_transform,
                  (Log, Standardize, ChainedOutcomeTransform),
              )
          else:
              assert not hasattr(m, "outcome_transform")
  
      # test constructing likelihood wrapper
      mll = SumMarginalLogLikelihood(model.likelihood, model)
      for mll_ in mll.mlls:
          self.assertIsInstance(mll_, ExactMarginalLogLikelihood)
  
      # test model fitting (sequential)
      with warnings.catch_warnings():
          warnings.filterwarnings(
              "ignore", category=OptimizationWarning
          )
          mll = fit_gpytorch_mll(
              mll,
              optimizer_kwargs={"options": {"maxiter": 1}},
              max_attempts=1,
          )
      with warnings.catch_warnings():
          warnings.filterwarnings(
              "ignore", category=OptimizationWarning
          )
          # test model fitting (joint)
          mll = fit_gpytorch_mll(
              mll,
              optimizer_kwargs={"options": {"maxiter": 1}},
              max_attempts=1,
              sequential=False,
          )
  
      # test subset outputs
      subset_model = model.subset_output([1])
      self.assertIsInstance(subset_model, ModelListGP)
      self.assertEqual(len(subset_model.models), 1)
      sd_subset = subset_model.models[0].state_dict()
      sd = model.models[1].state_dict()
      self.assertTrue(set(sd_subset.keys()) == set(sd.keys()))
      self.assertTrue(
          all(torch.equal(v, sd[k]) for k, v in sd_subset.items())
      )
  
      # test posterior
      test_x = torch.tensor([[0.25], [0.75]], **tkwargs)
      posterior = model.posterior(test_x)
      gpytorch_posterior_expected = outcome_transform in (
          "None",
          "Standardize",
      )
      expected_type = (
          GPyTorchPosterior
          if gpytorch_posterior_expected
          else PosteriorList
      )
      self.assertIsInstance(posterior, expected_type)
      submodel = model.models[0]
      p0 = submodel.posterior(test_x)
      self.assertAllClose(posterior.mean[:, [0]], p0.mean)
      self.assertAllClose(posterior.variance[:, [0]], p0.variance)
  
      if gpytorch_posterior_expected:
          self.assertIsInstance(
              posterior.distribution, MultitaskMultivariateNormal
          )
      if outcome_transform != "None":
          # ensure un-transformation is applied
          submodel = model.models[0]
          p0 = submodel.posterior(test_x)
          tmp_tf = submodel.outcome_transform
          del submodel.outcome_transform
          p0_tf = submodel.posterior(test_x)
          submodel.outcome_transform = tmp_tf
          expected_var = tmp_tf.untransform_posterior(p0_tf).variance
          self.assertAllClose(p0.variance, expected_var)
  
      # test output_indices
      posterior = model.posterior(
          test_x, output_indices=[0], observation_noise=True
      )
      self.assertIsInstance(posterior, expected_type)
      if gpytorch_posterior_expected:
          self.assertIsInstance(
              posterior.distribution, MultivariateNormal
          )
  
      # test condition_on_observations
      f_x = [torch.rand(2, 1, **tkwargs) for _ in range(2)]
      f_y = torch.rand(2, 2, **tkwargs)
      if fixed_noise:
          noise = 0.1 + 0.1 * torch.rand_like(f_y)
          cond_kwargs = {"noise": noise}
      else:
          cond_kwargs = {}
      cm = model.condition_on_observations(f_x, f_y, **cond_kwargs)
      self.assertIsInstance(cm, ModelListGP)
  
      # test condition_on_observations batched
      f_x = [torch.rand(3, 2, 1, **tkwargs) for _ in range(2)]
      f_y = torch.rand(3, 2, 2, **tkwargs)
      cm = model.condition_on_observations(f_x, f_y, **cond_kwargs)
      self.assertIsInstance(cm, ModelListGP)
  
      # test condition_on_observations batched (fast fantasies)
      f_x = [torch.rand(2, 1, **tkwargs) for _ in range(2)]
      f_y = torch.rand(3, 2, 2, **tkwargs)
      cm = model.condition_on_observations(f_x, f_y, **cond_kwargs)
      self.assertIsInstance(cm, ModelListGP)
  
      # test condition_on_observations (incorrect input shape error)
      with self.assertRaises(BotorchTensorDimensionError):
          model.condition_on_observations(
              f_x, torch.rand(3, 2, 3, **tkwargs), **cond_kwargs
          )
  
      # test X having wrong size
      with self.assertRaises(BotorchTensorDimensionError):
          model.condition_on_observations(f_x[:1], f_y)
  
      # test posterior transform
      X = torch.rand(3, 1, **tkwargs)
      weights = torch.tensor([1, 2], **tkwargs)
      post_tf = ScalarizedPosteriorTransform(weights=weights)
      if gpytorch_posterior_expected:
          posterior_tf = model.posterior(X, posterior_transform=post_tf)
          self.assertTrue(
              torch.allclose(
                  posterior_tf.mean,
                  model.posterior(X).mean @ weights.unsqueeze(-1),
              )
          )
  
      return model
  
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 1 for calling the TestModelListGP obj's underlying member method code with example usage: obj._base_test_ModelListGP(fixed_noise, dtype, outcome_transform) and returns: model