class_docstr: Posterior class for a Higher order Gaussian process model [Zhe2019hogp]_. Extends
  the standard GPyTorch posterior class by overwriting the rsample method.
  The posterior variance is handled internally by the HigherOrderGP model.
  HOGP is a tensorized GP model so the posterior covariance grows to be extremely
  large, but is highly structured, which means that we can exploit Kronecker
  identities to sample from the posterior using Matheron's rule as described in
  [Doucet2010sampl]_.
  
  In general, this posterior should ONLY be used for HOGP models
  that have highly structured covariances. It should also only be used internally when
  called from the HigherOrderGP.posterior(...) method. At this time, the posterior
  does not support gradients with respect to the training data.
docstr: The t-batch range.
  
  This is used in samplers to identify the t-batch component of the
  `base_sample_shape`. The base samples are expanded over the t-batches to
  provide consistency in the acquisition values, i.e., to ensure that a
  candidate produces same value regardless of its position on the t-batch.
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code: def batch_range(self) -> Tuple[int, int]:
      r"""The t-batch range.
  
      This is used in samplers to identify the t-batch component of the
      `base_sample_shape`. The base samples are expanded over the t-batches to
      provide consistency in the acquisition values, i.e., to ensure that a
      candidate produces same value regardless of its position on the t-batch.
      """
      return (0, -1)
  
file_path: botorch/botorch/posteriors/higher_order.py
imports: from typing import Optional, Tuple
  import torch
  from botorch.exceptions.errors import BotorchTensorDimensionError
  from botorch.posteriors.gpytorch import GPyTorchPosterior
  from gpytorch.distributions import MultivariateNormal
  from linear_operator.operators import LinearOperator
  from torch import Tensor
label_desc: Use image node_id 3 for calling the HigherOrderGPPosterior obj's underlying member method code with example usage: obj.batch_range() and returns: int,  unknown