code: def test_fit_model(self):
      for infer_noise, dtype in itertools.product(
          [True, False], [torch.float, torch.double]
      ):
          tkwargs = {"device": self.device, "dtype": dtype}
          (
              train_X,
              train_Y,
              train_Yvar,
              model,
          ) = self._get_data_and_model(
              infer_noise=infer_noise, **tkwargs
          )
          n, d = train_X.shape
  
          # Test init
          self.assertIsNone(model.mean_module)
          self.assertIsNone(model.covar_module)
          self.assertIsNone(model.likelihood)
          self.assertIsInstance(model.pyro_model, SaasPyroModel)
          self.assertAllClose(train_X, model.pyro_model.train_X)
          self.assertAllClose(train_Y, model.pyro_model.train_Y)
          if infer_noise:
              self.assertIsNone(model.pyro_model.train_Yvar)
          else:
              self.assertAllClose(
                  train_Yvar.clamp(MIN_INFERRED_NOISE_LEVEL),
                  model.pyro_model.train_Yvar,
              )
  
          # Fit a model and check that the hyperparameters have the correct shape
          fit_fully_bayesian_model_nuts(
              model,
              warmup_steps=8,
              num_samples=5,
              thinning=2,
              disable_progbar=True,
          )
          self.assertEqual(model.batch_shape, torch.Size([3]))
          self.assertEqual(model._aug_batch_shape, torch.Size([3]))
          # Using mock here since multi-output is currently not supported.
          with mock.patch.object(model, "_num_outputs", 2):
              self.assertEqual(
                  model._aug_batch_shape, torch.Size([3, 2])
              )
          self.assertIsInstance(model.mean_module, ConstantMean)
          self.assertEqual(
              model.mean_module.raw_constant.shape, model.batch_shape
          )
          self.assertIsInstance(model.covar_module, ScaleKernel)
          self.assertEqual(
              model.covar_module.outputscale.shape, model.batch_shape
          )
          self.assertIsInstance(
              model.covar_module.base_kernel, MaternKernel
          )
          self.assertEqual(
              model.covar_module.base_kernel.lengthscale.shape,
              torch.Size([3, 1, d]),
          )
          self.assertIsInstance(
              model.likelihood,
              GaussianLikelihood
              if infer_noise
              else FixedNoiseGaussianLikelihood,
          )
          if infer_noise:
              self.assertEqual(
                  model.likelihood.noise.shape, torch.Size([3, 1])
              )
          else:
              self.assertEqual(
                  model.likelihood.noise.shape, torch.Size([3, n])
              )
              self.assertAllClose(
                  train_Yvar.clamp(MIN_INFERRED_NOISE_LEVEL)
                  .squeeze(-1)
                  .repeat(3, 1),
                  model.likelihood.noise,
              )
  
          # Predict on some test points
          for batch_shape in [[5], [6, 5, 2]]:
              test_X = torch.rand(*batch_shape, d, **tkwargs)
              posterior = model.posterior(test_X)
              self.assertIsInstance(posterior, GaussianMixturePosterior)
              # Mean/variance
              expected_shape = (
                  *batch_shape[: MCMC_DIM + 2],
                  *model.batch_shape,
                  *batch_shape[MCMC_DIM + 2 :],
                  1,
              )
              expected_shape = torch.Size(expected_shape)
              mean, var = posterior.mean, posterior.variance
              self.assertEqual(mean.shape, expected_shape)
              self.assertEqual(var.shape, expected_shape)
              # Mixture mean/variance/median/quantiles
              mixture_mean = posterior.mixture_mean
              mixture_variance = posterior.mixture_variance
              quantile1 = posterior.quantile(value=torch.tensor(0.01))
              quantile2 = posterior.quantile(value=torch.tensor(0.99))
              self.assertEqual(
                  mixture_mean.shape, torch.Size(batch_shape + [1])
              )
              self.assertEqual(
                  mixture_variance.shape, torch.Size(batch_shape + [1])
              )
              self.assertTrue(mixture_variance.min() > 0.0)
              self.assertEqual(
                  quantile1.shape, torch.Size(batch_shape + [1])
              )
              self.assertEqual(
                  quantile2.shape, torch.Size(batch_shape + [1])
              )
              self.assertTrue((quantile2 > quantile1).all())
              quantile12 = posterior.quantile(
                  value=torch.tensor([0.01, 0.99])
              )
              self.assertAllClose(
                  quantile12, torch.stack([quantile1, quantile2], dim=0)
              )
              dist = torch.distributions.Normal(
                  loc=posterior.mean, scale=posterior.variance.sqrt()
              )
              self.assertAllClose(
                  dist.cdf(quantile1.unsqueeze(MCMC_DIM)).mean(
                      dim=MCMC_DIM
                  ),
                  torch.full(batch_shape + [1], 0.01, **tkwargs),
                  atol=1e-6,
              )
              self.assertAllClose(
                  dist.cdf(quantile2.unsqueeze(MCMC_DIM)).mean(
                      dim=MCMC_DIM
                  ),
                  torch.full(batch_shape + [1], 0.99, **tkwargs),
                  atol=1e-6,
              )
              # Invalid quantile should raise
              for q in [-1.0, 0.0, 1.0, 1.3333]:
                  with self.assertRaisesRegex(
                      ValueError, "value is expected to be in the range"
                  ):
                      posterior.quantile(value=torch.tensor(q))
  
              # Test model lists with fully Bayesian models and mixed modeling
              deterministic = GenericDeterministicModel(
                  f=lambda x: x[..., :1]
              )
              for ModelListClass, model2 in zip(
                  [ModelList, ModelListGP], [deterministic, model]
              ):
                  expected_shape = (
                      *batch_shape[: MCMC_DIM + 2],
                      *model.batch_shape,
                      *batch_shape[MCMC_DIM + 2 :],
                      2,
                  )
                  expected_shape = torch.Size(expected_shape)
                  model_list = ModelListClass(model, model2)
                  posterior = model_list.posterior(test_X)
                  mean, var = posterior.mean, posterior.variance
                  self.assertEqual(mean.shape, expected_shape)
                  self.assertEqual(var.shape, expected_shape)
              # This check is only for ModelListGP.
              self.assertEqual(
                  model_list.batch_shape, model.batch_shape
              )
  
          # Mixing fully Bayesian models with different batch shapes isn't supported
          _, _, _, model2 = self._get_data_and_model(
              infer_noise=infer_noise, **tkwargs
          )
          fit_fully_bayesian_model_nuts(
              model2,
              warmup_steps=1,
              num_samples=1,
              thinning=1,
              disable_progbar=True,
          )
          with self.assertRaisesRegex(
              NotImplementedError, "All MCMC batch dimensions"
          ):
              ModelList(model, model2).posterior(
                  test_X
              )._extended_shape()
          with self.assertRaisesRegex(
              NotImplementedError,
              "All MCMC batch dimensions must have the same size, got",
          ):
              ModelList(model, model2).posterior(test_X).mean
  
          # Check properties
          median_lengthscale = model.median_lengthscale
          self.assertEqual(median_lengthscale.shape, torch.Size([4]))
          self.assertEqual(model.num_mcmc_samples, 3)
  
          # Check the keys in the state dict
          true_keys = (
              EXPECTED_KEYS_NOISE if infer_noise else EXPECTED_KEYS
          )
          self.assertEqual(
              set(model.state_dict().keys()), set(true_keys)
          )
  
          for i in range(2):  # Test loading via state dict
              m = model if i == 0 else ModelList(model, deterministic)
              state_dict = m.state_dict()
              _, _, _, m_new = self._get_data_and_model(
                  infer_noise=infer_noise, **tkwargs
              )
              m_new = (
                  m_new if i == 0 else ModelList(m_new, deterministic)
              )
              if i == 0:
                  self.assertEqual(m_new.state_dict(), {})
              m_new.load_state_dict(state_dict)
              self.assertEqual(
                  m.state_dict().keys(), m_new.state_dict().keys()
              )
              for k in m.state_dict().keys():
                  self.assertTrue(
                      (m.state_dict()[k] == m_new.state_dict()[k]).all()
                  )
              preds1, preds2 = m.posterior(test_X), m_new.posterior(
                  test_X
              )
              self.assertTrue(torch.equal(preds1.mean, preds2.mean))
              self.assertTrue(
                  torch.equal(preds1.variance, preds2.variance)
              )
  
          # Make sure the model shapes are set correctly
          self.assertEqual(
              model.pyro_model.train_X.shape, torch.Size([n, d])
          )
          self.assertAllClose(model.pyro_model.train_X, train_X)
          model.train()  # Put the model in train mode
          self.assertAllClose(train_X, model.pyro_model.train_X)
          self.assertIsNone(model.mean_module)
          self.assertIsNone(model.covar_module)
          self.assertIsNone(model.likelihood)
  
imports: import itertools
  from unittest import mock
  from unittest.mock import patch
  import pyro
  import torch
  from botorch import fit_fully_bayesian_model_nuts, utils
  from botorch.acquisition.analytic import ExpectedImprovement, PosteriorMean, ProbabilityOfImprovement, UpperConfidenceBound
  from botorch.acquisition.logei import qLogExpectedImprovement, qLogNoisyExpectedImprovement
  from botorch.acquisition.monte_carlo import qExpectedImprovement, qNoisyExpectedImprovement, qProbabilityOfImprovement, qSimpleRegret, qUpperConfidenceBound
  from botorch.acquisition.multi_objective import prune_inferior_points_multi_objective, qExpectedHypervolumeImprovement, qNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.multi_objective.logei import qLogExpectedHypervolumeImprovement, qLogNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.utils import prune_inferior_points
  from botorch.models import ModelList, ModelListGP
  from botorch.models.deterministic import GenericDeterministicModel
  from botorch.models.fully_bayesian import MCMC_DIM, MIN_INFERRED_NOISE_LEVEL, PyroModel, SaasFullyBayesianSingleTaskGP, SaasPyroModel
  from botorch.models.transforms import Normalize, Standardize
  from botorch.posteriors.fully_bayesian import batched_bisect, GaussianMixturePosterior
  from botorch.sampling.get_sampler import get_sampler
  from botorch.utils.datasets import SupervisedDataset
  from botorch.utils.multi_objective.box_decompositions.non_dominated import NondominatedPartitioning
  from botorch.utils.safe_math import logmeanexp
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.kernels import MaternKernel, ScaleKernel
  from gpytorch.likelihoods import FixedNoiseGaussianLikelihood, GaussianLikelihood
  from gpytorch.means import ConstantMean
  from linear_operator.operators import to_linear_operator
  from pyro.ops.integrator import _EXCEPTION_HANDLERS, potential_grad, register_exception_handler
label_desc: Use image node_id 6 for calling the TestFullyBayesianSingleTaskGP obj's underlying member method code with example usage: obj.test_fit_model() without return types