code: def testMultipleCorrelatedStatesWithOneBatchDim(
      self, asserts, use_untempered_fn
  ):
      dtype = np.float32
      true_mean = dtype([0, 0])
      true_cov = dtype([[1, 0.5], [0.5, 1]])
      # Use LinearOperatorLowerTriangular to get broadcasting ability.
      linop = tf.linalg.LinearOperatorLowerTriangular(
          tf.linalg.cholesky(true_cov)
      )
  
      def target_log_prob(x, y):
          # Corresponds to unnormalized MVN.
          # z = matmul(inv(chol(true_cov)), [x, y] - true_mean)
          xy = tf.stack([x, y], axis=-1) - true_mean
          z = linop.solvevec(xy)
          return -0.5 * tf.reduce_sum(z**2.0, axis=-1)
  
      if use_untempered_fn:
          # Should not change results at all
          untempered_log_prob_fn = lambda x, unused_y: tf.zeros_like(x)
          tempered_log_prob_fn = target_log_prob
          target_log_prob = None
      else:
          untempered_log_prob_fn = None
          tempered_log_prob_fn = None
  
      def make_kernel_fn(target_log_prob_fn):
          return hmc.HamiltonianMonteCarlo(
              target_log_prob_fn=target_log_prob_fn,
              step_size=[0.75, 0.75],
              num_leapfrog_steps=3,
          )
  
      remc = replica_exchange_mc.ReplicaExchangeMC(
          target_log_prob_fn=target_log_prob,
          inverse_temperatures=[1.0, 0.9, 0.8],
          make_kernel_fn=make_kernel_fn,
          untempered_log_prob_fn=untempered_log_prob_fn,
          tempered_log_prob_fn=tempered_log_prob_fn,
      )
  
      num_results = 13
      if asserts:
          num_results = 2000
          remc.one_step = tf.function(remc.one_step, autograph=False)
  
      states = sample.sample_chain(
          num_results=num_results,
          # batch_shape = [4] for each initial state
          current_state=[tf.ones(4), tf.ones(4)],
          kernel=remc,
          num_burnin_steps=400,
          trace_fn=None,
          seed=test_util.test_seed(),
      )
  
      states = tf.stack(states, axis=-1)
      self.assertAllEqual((num_results, 4, 2), states.shape)
  
      states_, ess_, cov_ = self.evaluate(
          [
              states,
              effective_sample_size(states),
              sample_stats.covariance(states),
          ]
      )
  
      if not asserts:
          return
  
      self.assertGreater(
          np.min(ess_), num_results / 10, "Bad sampling found!"
      )
  
      # 6 standard errors for mean/variance estimates.
      mean_atol = 8 / np.sqrt(np.min(ess_))
      cov_atol = 8 * np.sqrt(2) / np.sqrt(np.min(ess_))
  
      self.assertAllClose(
          true_mean, states_[:, 0, :].mean(axis=0), atol=mean_atol
      )
      self.assertAllClose(
          true_mean, states_[:, 1, :].mean(axis=0), atol=mean_atol
      )
      self.assertAllClose(true_cov, cov_[0], atol=cov_atol)
      self.assertAllClose(true_cov, cov_[1], atol=cov_atol)
  
imports: from absl import logging
  from absl.testing import parameterized
  import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import categorical
  from tensorflow_probability.python.distributions import mixture_same_family
  from tensorflow_probability.python.distributions import mvn_diag
  from tensorflow_probability.python.distributions import normal
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import test_combinations
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.internal import unnest
  from tensorflow_probability.python.mcmc import diagnostic
  from tensorflow_probability.python.mcmc import hmc
  from tensorflow_probability.python.mcmc import random_walk_metropolis
  from tensorflow_probability.python.mcmc import replica_exchange_mc
  from tensorflow_probability.python.mcmc import sample
  from tensorflow_probability.python.mcmc import simple_step_size_adaptation
  from tensorflow_probability.python.stats import sample_stats
label_desc: Use image node_id 8 for calling the REMCTest obj's underlying member method code with example usage: obj.testMultipleCorrelatedStatesWithOneBatchDim(asserts, use_untempered_fn) and returns: unknown, hmc