code: def single_task_pyro_model(
      X: Tensor,
      Y: Tensor,
      Yvar: Tensor,
      use_input_warping: bool = False,
      eps: float = 1e-7,
      gp_kernel: str = "matern",
      task_feature: Optional[int] = None,
      rank: Optional[int] = None,
  ) -> None:
      r"""Instantiates a single task pyro model for running fully bayesian inference.
  
      Args:
          X: A `n x d` tensor of input parameters.
          Y: A `n x 1` tensor of output.
          Yvar: A `n x 1` tensor of observed noise.
          use_input_warping: A boolean indicating whether to use input warping
          task_feature: Column index of task feature in X.
          gp_kernel: kernel name. Currently only two kernels are supported: "matern" for
              Matern Kernel and "rbf" for RBFKernel.
          rank: num of latent task features to learn for task covariance.
      """
      Y = Y.view(-1)
      Yvar = Yvar.view(-1)
      tkwargs = {"dtype": X.dtype, "device": X.device}
      dim = X.shape[-1]
      # TODO: test alternative outputscale priors
      outputscale = pyro_sample_outputscale(
          concentration=2.0, rate=0.15, **tkwargs
      )
      mean = pyro_sample_mean(**tkwargs)
      if torch.isnan(Yvar).all():
          # infer noise level
          noise = MIN_OBSERVED_NOISE_LEVEL + pyro_sample_noise(
              **tkwargs
          )
      else:
          noise = Yvar.clamp_min(MIN_OBSERVED_NOISE_LEVEL)
      # pyre-fixme[6]: For 2nd param expected `float` but got `Union[device, dtype]`.
      lengthscale = pyro_sample_saas_lengthscales(dim=dim, **tkwargs)
  
      # transform inputs through kumaraswamy cdf
      if use_input_warping:
          c0, c1 = pyro_sample_input_warping(dim=dim, **tkwargs)
          # unnormalize X from [0, 1] to [eps, 1-eps]
          X = (X * (1 - 2 * eps) + eps).clamp(eps, 1 - eps)
          X_tf = 1 - torch.pow((1 - torch.pow(X, c1)), c0)
      else:
          X_tf = X
      # compute kernel
      if gp_kernel == "matern":
          K = matern_kernel(X=X_tf, Z=X_tf, lengthscale=lengthscale)
      elif gp_kernel == "rbf":
          K = rbf_kernel(X=X_tf, Z=X_tf, lengthscale=lengthscale)
      else:
          raise ValueError(
              f"Expected kernel to be 'rbf' or 'matern', got {gp_kernel}"
          )
  
      # add noise
      K = outputscale * K + noise * torch.eye(
          X.shape[0], dtype=X.dtype, device=X.device
      )
  
      pyro.sample(
          "Y",
          # pyre-fixme[16]: Module `distributions` has no attribute `MultivariateNormal`.
          pyro.distributions.MultivariateNormal(
              loc=mean.view(-1).expand(X.shape[0]),
              covariance_matrix=K,
          ),
          obs=Y,
      )
  
imports: import math
  import sys
  import time
  import types
  import warnings
  from logging import Logger
  from typing import Any, Callable, Dict, List, Optional, Tuple
  import numpy
  import pyro
  import torch
  from ax.exceptions.core import AxError
  from ax.models.torch.botorch import BotorchModel, TAcqfConstructor, TBestPointRecommender, TModelConstructor, TModelPredictor, TOptimizer
  from ax.models.torch.botorch_defaults import get_qLogNEI, MIN_OBSERVED_NOISE_LEVEL, recommend_best_observed_point, scipy_optimizer
  from ax.models.torch.botorch_moo import MultiObjectiveBotorchModel
  from ax.models.torch.botorch_moo_defaults import get_qLogNEHVI, pareto_frontier_evaluator
  from ax.models.torch.frontier_utils import TFrontierEvaluator
  from ax.models.torch.fully_bayesian_model_utils import _get_single_task_gpytorch_model, load_mcmc_samples_to_model, pyro_sample_input_warping, pyro_sample_mean, pyro_sample_noise, pyro_sample_outputscale, pyro_sample_saas_lengthscales
  from ax.utils.common.docutils import copy_doc
  from ax.utils.common.logger import get_logger
  from ax.utils.common.typeutils import checked_cast
  from botorch.acquisition import AcquisitionFunction
  from botorch.models.gpytorch import GPyTorchModel
  from botorch.models.model import Model
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.posteriors.gpytorch import GPyTorchPosterior
  from botorch.utils.safe_math import logmeanexp
  from gpytorch.kernels.kernel import dist
  from torch import Tensor
label_desc: Use image node_id 5 for calling a global function with example usage: single_task_pyro_model(X, Y, Yvar, use_input_warping, eps, gp_kernel, task_feature, rank) without return types