code: def test_marginal_likelihood_gradients_are_defined(self):
      def marginal_log_likelihood(level_scale, noise_scale):
          _, _, _, lps = particle_filter.particle_filter(
              observations=tf.convert_to_tensor(
                  [1.0, 2.0, 3.0, 4.0, 5.0]
              ),
              initial_state_prior=normal.Normal(loc=0, scale=1.0),
              transition_fn=lambda _, x: normal.Normal(
                  loc=x, scale=level_scale
              ),
              observation_fn=lambda _, x: normal.Normal(
                  loc=x, scale=noise_scale
              ),
              num_particles=4,
              seed=test_util.test_seed(),
          )
          return tf.reduce_sum(lps)
  
      _, grads = gradient.value_and_gradient(
          marginal_log_likelihood, 1.0, 1.0
      )
      self.assertAllNotNone(grads)
      self.assertAllAssertsNested(self.assertNotAllZero, grads)
  
imports: import functools
  import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import shift
  from tensorflow_probability.python.distributions import bernoulli
  from tensorflow_probability.python.distributions import deterministic
  from tensorflow_probability.python.distributions import joint_distribution_auto_batched
  from tensorflow_probability.python.distributions import joint_distribution_named
  from tensorflow_probability.python.distributions import linear_gaussian_ssm
  from tensorflow_probability.python.distributions import mvn_diag
  from tensorflow_probability.python.distributions import mvn_tril
  from tensorflow_probability.python.distributions import normal
  from tensorflow_probability.python.distributions import poisson
  from tensorflow_probability.python.distributions import sample
  from tensorflow_probability.python.distributions import transformed_distribution
  from tensorflow_probability.python.distributions import uniform
  from tensorflow_probability.python.experimental.mcmc import particle_filter
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math import gradient
label_desc: Use image node_id 13 for calling the _ParticleFilterTest obj's underlying member method code with example usage: obj.test_marginal_likelihood_gradients_are_defined() and returns: tf