class_docstr: The standard likelihood for regression with support for missing values.
  Assumes a standard homoskedastic noise model:
  
  .. math::
      p(y \mid f) = f + \epsilon, \quad \epsilon \sim \mathcal N (0, \sigma^2)
  
  where :math:`\sigma^2` is a noise parameter. Values of y that are nan do
  not impact the likelihood calculation.
  
  .. note::
      This likelihood can be used for exact or approximate inference.
  
  .. warning::
      This likelihood is deprecated in favor of :class:`gpytorch.settings.observation_nan_policy`.
  
  :param noise_prior: Prior for noise parameter :math:`\sigma^2`.
  :type noise_prior: ~gpytorch.priors.Prior, optional
  :param noise_constraint: Constraint for noise parameter :math:`\sigma^2`.
  :type noise_constraint: ~gpytorch.constraints.Interval, optional
  :param batch_shape: The batch shape of the learned noise parameter (default: []).
  :type batch_shape: torch.Size, optional
  :var torch.Tensor noise: :math:`\sigma^2` parameter (noise)
  
  .. note::
      GaussianLikelihoodWithMissingObs has an analytic marginal distribution.
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code: def __init__(self, **kwargs: Any) -> None:
      warnings.warn(
          "GaussianLikelihoodWithMissingObs is replaced by gpytorch.settings.observation_nan_policy('fill').",
          DeprecationWarning,
      )
      super().__init__(**kwargs)
  
imports: import math
  import warnings
  from copy import deepcopy
  from typing import Any, Optional, Tuple, Union
  import torch
  from linear_operator.operators import LinearOperator, MaskedLinearOperator, ZeroLinearOperator
  from torch import Tensor
  from torch.distributions import Distribution, Normal
  from ..None import settings
  from ..constraints import Interval
  from ..distributions import base_distributions, MultivariateNormal
  from ..priors import Prior
  from ..utils.warnings import GPInputWarning
  from .likelihood import Likelihood
  from .noise_models import FixedGaussianNoise, HomoskedasticNoise, Noise
label_desc: Use image node_id 1 to create a new GaussianLikelihoodWithMissingObs object from inherited base classes: GaussianLikelihood with example: obj = GaussianLikelihoodWithMissingObs()