text: import torch
  
  import pyro
  import pyro.distributions as dist
  
  from .likelihood import Likelihood
  
  
  class Poisson(Likelihood):
      """
      Implementation of Poisson likelihood, which is used for count data.
  
      Poisson likelihood uses the :class:`~pyro.distributions.Poisson`
      distribution, so the output of ``response_function`` should be positive.
      By default, we use :func:`torch.exp` as response function, corresponding
      to a log-Gaussian Cox process.
  
      :param callable response_function: A mapping to positive real numbers.
      """
      def __init__(self, response_function=None):
          super(Poisson, self).__init__()
          self.response_function = torch.exp if response_function is None else response_function
  
      def forward(self, f_loc, f_var, y=None):
          r"""
          Samples :math:`y` given :math:`f_{loc}`, :math:`f_{var}` according to
  
              .. math:: f & \sim \mathbb{Normal}(f_{loc}, f_{var}),\\
                  y & \sim \mathbb{Poisson}(\exp(f)).
  
          .. note:: The log likelihood is estimated using Monte Carlo with 1 sample of
              :math:`f`.
  
          :param torch.Tensor f_loc: Mean of latent function output.
          :param torch.Tensor f_var: Variance of latent function output.
          :param torch.Tensor y: Training output tensor.
          :returns: a tensor sampled from likelihood
          :rtype: torch.Tensor
          """
          # calculates Monte Carlo estimate for E_q(f) [logp(y | f)]
          f = dist.Normal(f_loc, f_var.sqrt())()
          f_res = self.response_function(f)
  
          y_dist = dist.Poisson(f_res)
          if y is not None:
              y_dist = y_dist.expand_by(y.shape[:-f_res.dim()]).to_event(y.dim())
          return pyro.sample("y", y_dist, obs=y)
  