code: def sample_chain(
      num_results,
      current_state,
      previous_kernel_results=None,
      kernel=None,
      num_burnin_steps=0,
      num_steps_between_results=0,
      trace_fn=lambda current_state, kernel_results: kernel_results,
      return_final_kernel_results=False,
      parallel_iterations=10,
      seed=None,
      name=None,
  ):
      """Implements Markov chain Monte Carlo via repeated `TransitionKernel` steps.
  
      This function samples from an Markov chain at `current_state` and whose
      stationary distribution is governed by the supplied `TransitionKernel`
      instance (`kernel`).
  
      The `current_state` can be represented as a single `Tensor` or a `list` of
      `Tensors` which collectively represent the current state.
  
      This function can sample from multiple chains, in parallel.  Whether or not
      there are multiple chains is dictated by how the `kernel` treats its inputs.
      Typically, the shape of the independent chains is shape of the result of the
      `target_log_prob_fn` used by the `kernel` when applied to the given
      `current_state`.
  
      Since MCMC states are correlated, it is sometimes desirable to produce
      additional intermediate states, and then discard them, ending up with a set of
      states with decreased autocorrelation.  See [Owen (2017)][1]. Such 'thinning'
      is made possible by setting `num_steps_between_results > 0`. The chain then
      takes `num_steps_between_results` extra steps between the steps that make it
      into the results. The extra steps are never materialized, and thus do not
      increase memory requirements.
  
      In addition to returning the chain state, this function supports tracing of
      auxiliary variables used by the kernel. The traced values are selected by
      specifying `trace_fn`. By default, all kernel results are traced but in the
      future the default will be changed to no results being traced, so plan
      accordingly. See below for some examples of this feature.
  
      Args:
        num_results: Integer number of Markov chain draws.
        current_state: `Tensor` or Python `list` of `Tensor`s representing the
          current state(s) of the Markov chain(s).
        previous_kernel_results: A `Tensor` or a nested collection of `Tensor`s
          representing internal calculations made within the previous call to this
          function (or as returned by `bootstrap_results`).
        kernel: An instance of `tfp.mcmc.TransitionKernel` which implements one step
          of the Markov chain.
        num_burnin_steps: Integer number of chain steps to take before starting to
          collect results.
          Default value: 0 (i.e., no burn-in).
        num_steps_between_results: Integer number of chain steps between collecting
          a result. Only one out of every `num_steps_between_samples + 1` steps is
          included in the returned results.  The number of returned chain states is
          still equal to `num_results`.  Default value: 0 (i.e., no thinning).
        trace_fn: A callable that takes in the current chain state and the previous
          kernel results and return a `Tensor` or a nested collection of `Tensor`s
          that is then traced along with the chain state.
        return_final_kernel_results: If `True`, then the final kernel results are
          returned alongside the chain state and the trace specified by the
          `trace_fn`.
        parallel_iterations: The number of iterations allowed to run in parallel. It
          must be a positive integer. See `tf.while_loop` for more details.
        seed: PRNG seed; see `tfp.random.sanitize_seed` for details.
        name: Python `str` name prefixed to Ops created by this function.
          Default value: `None` (i.e., 'mcmc_sample_chain').
  
      Returns:
        checkpointable_states_and_trace: if `return_final_kernel_results` is
          `True`. The return value is an instance of
          `CheckpointableStatesAndTrace`.
        all_states: if `return_final_kernel_results` is `False` and `trace_fn` is
          `None`. The return value is a `Tensor` or Python list of `Tensor`s
          representing the state(s) of the Markov chain(s) at each result step. Has
          same shape as input `current_state` but with a prepended
          `num_results`-size dimension.
        states_and_trace: if `return_final_kernel_results` is `False` and
          `trace_fn` is not `None`. The return value is an instance of
          `StatesAndTrace`.
  
      #### Examples
  
      ##### Sample from a diagonal-variance Gaussian.
  
      I.e.,
  
      ```none
      for i=1..n:
        x[i] ~ MultivariateNormal(loc=0, scale=diag(true_stddev))  # likelihood
      ```
  
      ```python
      import tensorflow as tf
      import tensorflow_probability as tfp
      tfd = tfp.distributions
  
      dims = 10
      true_stddev = tf.sqrt(tf.linspace(1., 3., dims))
      likelihood = tfd.MultivariateNormalDiag(loc=0., scale_diag=true_stddev)
  
      states = tfp.mcmc.sample_chain(
          num_results=1000,
          num_burnin_steps=500,
          current_state=tf.zeros(dims),
          kernel=tfp.mcmc.HamiltonianMonteCarlo(
            target_log_prob_fn=likelihood.log_prob,
            step_size=0.5,
            num_leapfrog_steps=2),
          trace_fn=None)
  
      sample_mean = tf.reduce_mean(states, axis=0)
      # ==> approx all zeros
  
      sample_stddev = tf.sqrt(tf.reduce_mean(
          tf.squared_difference(states, sample_mean),
          axis=0))
      # ==> approx equal true_stddev
      ```
  
      ##### Sampling from factor-analysis posteriors with known factors.
  
      I.e.,
  
      ```none
      # prior
      w ~ MultivariateNormal(loc=0, scale=eye(d))
      for i=1..n:
        # likelihood
        x[i] ~ Normal(loc=w^T F[i], scale=1)
      ```
  
      where `F` denotes factors.
  
      ```python
      import tensorflow as tf
      import tensorflow_probability as tfp
      tfd = tfp.distributions
  
      # Specify model.
      def make_prior(dims):
        return tfd.MultivariateNormalDiag(
            loc=tf.zeros(dims))
  
      def make_likelihood(weights, factors):
        return tfd.MultivariateNormalDiag(
            loc=tf.matmul(weights, factors, adjoint_b=True))
  
      def joint_log_prob(num_weights, factors, x, w):
        return (make_prior(num_weights).log_prob(w) +
                make_likelihood(w, factors).log_prob(x))
  
      def unnormalized_log_posterior(w):
        # Posterior is proportional to: `p(W, X=x | factors)`.
        return joint_log_prob(num_weights, factors, x, w)
  
      # Setup data.
      num_weights = 10 # == d
      num_factors = 40 # == n
      num_chains = 100
  
      weights = make_prior(num_weights).sample(1)
      factors = tf.random.normal([num_factors, num_weights])
      x = make_likelihood(weights, factors).sample()
  
      # Sample from Hamiltonian Monte Carlo Markov Chain.
  
      # Get `num_results` samples from `num_chains` independent chains.
      chains_states, kernels_results = tfp.mcmc.sample_chain(
          num_results=1000,
          num_burnin_steps=500,
          current_state=tf.zeros([num_chains, num_weights], name='init_weights'),
          kernel=tfp.mcmc.HamiltonianMonteCarlo(
            target_log_prob_fn=unnormalized_log_posterior,
            step_size=0.1,
            num_leapfrog_steps=2))
  
      # Compute sample stats.
      sample_mean = tf.reduce_mean(chains_states, axis=[0, 1])
      # ==> approx equal to weights
  
      sample_var = tf.reduce_mean(
          tf.squared_difference(chains_states, sample_mean),
          axis=[0, 1])
      # ==> less than 1
      ```
  
      ##### Custom tracing functions.
  
      ```python
      import tensorflow as tf
      import tensorflow_probability as tfp
      tfd = tfp.distributions
  
      likelihood = tfd.Normal(loc=0., scale=1.)
  
      def sample_chain(trace_fn):
        return tfp.mcmc.sample_chain(
          num_results=1000,
          num_burnin_steps=500,
          current_state=0.,
          kernel=tfp.mcmc.HamiltonianMonteCarlo(
            target_log_prob_fn=likelihood.log_prob,
            step_size=0.5,
            num_leapfrog_steps=2),
          trace_fn=trace_fn)
  
      def trace_log_accept_ratio(states, previous_kernel_results):
        return previous_kernel_results.log_accept_ratio
  
      def trace_everything(states, previous_kernel_results):
        return previous_kernel_results
  
      _, log_accept_ratio = sample_chain(trace_fn=trace_log_accept_ratio)
      _, kernel_results = sample_chain(trace_fn=trace_everything)
  
      acceptance_prob = tf.math.exp(tf.minimum(log_accept_ratio, 0.))
      # Equivalent to, but more efficient than:
      acceptance_prob = tf.math.exp(tf.minimum(
          kernel_results.log_accept_ratio, 0.))
      ```
  
      #### References
  
      [1]: Art B. Owen. Statistically efficient thinning of a Markov chain sampler.
           _Technical Report_, 2017.
           http://statweb.stanford.edu/~owen/reports/bestthinning.pdf
      """
      is_seeded = seed is not None
      seed = samplers.sanitize_seed(seed, salt="mcmc.sample_chain")
  
      if not kernel.is_calibrated:
          warnings.warn(
              "supplied `TransitionKernel` is not calibrated. Markov "
              "chain may not converge to intended target distribution."
          )
      with tf.name_scope(name or "mcmc_sample_chain"):
          num_results = ps.convert_to_shape_tensor(
              num_results, dtype=tf.int32, name="num_results"
          )
          num_burnin_steps = ps.convert_to_shape_tensor(
              num_burnin_steps, dtype=tf.int32, name="num_burnin_steps"
          )
          num_steps_between_results = ps.convert_to_shape_tensor(
              num_steps_between_results,
              dtype=tf.int32,
              name="num_steps_between_results",
          )
          current_state = tf.nest.map_structure(
              lambda x: tf.convert_to_tensor(x, name="current_state"),
              current_state,
          )
          if previous_kernel_results is None:
              previous_kernel_results = kernel.bootstrap_results(
                  current_state
              )
  
          if trace_fn is None:
              # It simplifies the logic to use a dummy function here.
              trace_fn = lambda *args: ()
              no_trace = True
          else:
              no_trace = False
          if trace_fn is sample_chain.__defaults__[4]:
              warnings.warn(
                  "Tracing all kernel results by default is deprecated. Set "
                  "the `trace_fn` argument to None (the future default "
                  "value) or an explicit callback that traces the values "
                  "you are interested in."
              )
  
          def _seeded_one_step(seed, *state_and_results):
              step_seed, passalong_seed = (
                  samplers.split_seed(seed)
                  if is_seeded
                  else (None, seed)
              )
              one_step_kwargs = (
                  dict(seed=step_seed) if is_seeded else {}
              )
              return [passalong_seed] + list(
                  kernel.one_step(*state_and_results, **one_step_kwargs)
              )
  
          def _trace_scan_fn(seed_state_and_results, num_steps):
              (
                  seed,
                  next_state,
                  current_kernel_results,
              ) = loop_util.smart_for_loop(
                  loop_num_iter=num_steps,
                  body_fn=_seeded_one_step,
                  initial_loop_vars=list(seed_state_and_results),
                  parallel_iterations=parallel_iterations,
              )
              return seed, next_state, current_kernel_results
  
          (_, _, final_kernel_results), (
              all_states,
              trace,
          ) = loop_util.trace_scan(
              loop_fn=_trace_scan_fn,
              initial_state=(
                  seed,
                  current_state,
                  previous_kernel_results,
              ),
              elems=tf.one_hot(
                  indices=0,
                  depth=num_results,
                  on_value=1 + num_burnin_steps,
                  off_value=1 + num_steps_between_results,
                  dtype=tf.int32,
              ),
              # pylint: disable=g-long-lambda
              trace_fn=lambda seed_state_and_results: (
                  seed_state_and_results[1],
                  trace_fn(*seed_state_and_results[1:]),
              ),
              # pylint: enable=g-long-lambda
              parallel_iterations=parallel_iterations,
          )
  
          if return_final_kernel_results:
              return CheckpointableStatesAndTrace(
                  all_states=all_states,
                  trace=trace,
                  final_kernel_results=final_kernel_results,
              )
          else:
              if no_trace:
                  return all_states
              else:
                  return StatesAndTrace(
                      all_states=all_states, trace=trace
                  )
  
file_path: probability/tensorflow_probability/python/mcmc/sample.py
imports: import collections
  import warnings
  import tensorflow.compat.v2
  from tensorflow_probability.python.internal import loop_util
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.mcmc.internal import util
label_desc: Use image node_id 1 for calling a global function with example usage: sample_chain(num_results, current_state, previous_kernel_results, kernel, num_burnin_steps, num_steps_between_results, trace_fn, return_final_kernel_results, parallel_iterations, seed, name) and returns: unknown, seed,  next_state,  current_kernel_results, CheckpointableStatesAndTrace, all_states, StatesAndTrace