class_docstr: A fully Bayesian multi-task GP model with the SAAS prior.
  
  This model assumes that the inputs have been normalized to [0, 1]^d and that the
  output has been stratified standardized to have zero mean and unit variance for
  each task.The SAAS model [Eriksson2021saasbo]_ with a Matern-5/2 is used as data
  kernel by default.
  
  You are expected to use `fit_fully_bayesian_model_nuts` to fit this model as it
  isn't compatible with `fit_gpytorch_model`.
  
  Example:
      >>> X1, X2 = torch.rand(10, 2), torch.rand(20, 2)
      >>> i1, i2 = torch.zeros(10, 1), torch.ones(20, 1)
      >>> train_X = torch.cat([
      >>>     torch.cat([X1, i1], -1), torch.cat([X2, i2], -1),
      >>> ])
      >>> train_Y = torch.cat(f1(X1), f2(X2)).unsqueeze(-1)
      >>> train_Yvar = 0.01 * torch.ones_like(train_Y)
      >>> mtsaas_gp = SaasFullyBayesianMultiTaskGP(
      >>>     train_X, train_Y, train_Yvar, task_feature=-1,
      >>> )
      >>> fit_fully_bayesian_model_nuts(mtsaas_gp)
      >>> posterior = mtsaas_gp.posterior(test_X)
code: def fantasize(self, *args, **kwargs) -> NoReturn:
      raise NotImplementedError("Fantasize is not implemented!")
  
imports: from typing import Any, Dict, List, Mapping, NoReturn, Optional, Tuple, Union
  import pyro
  import torch
  from botorch.acquisition.objective import PosteriorTransform
  from botorch.models.fully_bayesian import matern52_kernel, MIN_INFERRED_NOISE_LEVEL, PyroModel, reshape_and_detach, SaasPyroModel
  from botorch.models.multitask import MultiTaskGP
  from botorch.models.transforms.input import InputTransform
  from botorch.models.transforms.outcome import OutcomeTransform
  from botorch.posteriors.fully_bayesian import GaussianMixturePosterior, MCMC_DIM
  from botorch.utils.datasets import MultiTaskDataset, SupervisedDataset
  from gpytorch.distributions.multivariate_normal import MultivariateNormal
  from gpytorch.kernels import MaternKernel
  from gpytorch.kernels.kernel import Kernel
  from gpytorch.likelihoods.likelihood import Likelihood
  from gpytorch.means.mean import Mean
  from torch import Tensor
  from torch.nn.parameter import Parameter
label_desc: Use image node_id 6 for calling the SaasFullyBayesianMultiTaskGP obj's underlying member method code with example usage: obj.fantasize() without return types