code: def posterior(self, obs):
      concentration1 = self._latent.concentration1
      concentration0 = self._latent.concentration0
      total_count = self._conditional.total_count
      reduce_dims = len(obs.size()) - len(concentration1.size())
      # Unexpand total_count to have the same shape as concentration0.
      # Raise exception if this isn't possible.
      total_count = sum_leftmost(total_count, reduce_dims)
      summed_obs = sum_leftmost(obs, reduce_dims)
      return dist.Beta(
          concentration1 + summed_obs,
          total_count + concentration0 - summed_obs,
          validate_args=self._latent._validate_args,
      )
  
imports: from collections import defaultdict
  import torch
  import pyro.distributions
  from pyro import poutine
  from pyro.distributions.util import sum_leftmost
  from pyro.poutine.messenger import Messenger
  from pyro.poutine.util import site_is_subsample
label_desc: Use image node_id 4 for calling the BetaBinomialPair obj's underlying member method code with example usage: obj.posterior(obs) and returns: dist