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).

mcmc_sample_chain(
  kernel = NULL,
  num_results,
  current_state,
  previous_kernel_results = NULL,
  num_burnin_steps = 0,
  num_steps_between_results = 0,
  trace_fn = NULL,
  return_final_kernel_results = FALSE,
  parallel_iterations = 10,
  seed = NULL,
  name = NULL
)

Arguments

kernel	An instance of tfp$mcmc$TransitionKernel which implements one step of the Markov chain.
num_results	Integer number of Markov chain draws.
current_state	Tensor or list of Tensors representing the current state(s) of the Markov chain(s).
previous_kernel_results	A Tensor or a nested collection of Tensors representing internal calculations made within the previous call to this function (or as returned by bootstrap_results).
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 function that takes in the current chain state and the previous kernel results and return a Tensor or a nested collection of Tensors 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	Optional, a seed for reproducible sampling.
name	string prefixed to Ops created by this function. Default value: NULL, (i.e., "mcmc_sample_chain").

Value

list of:

• 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 NULL. The return value is a Tensor or Python list of Tensors 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 NULL. The return value is an instance of StatesAndTrace.

Details

This function can sample from multiple chains, in parallel. (Whether or not there are multiple chains is dictated by the kernel.)

The current_state can be represented as a single Tensor or a list of Tensors which collectively represent the 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). 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 (in calls to sess$run), and thus do not increase memory requirements.

Warning: when setting a seed in the kernel, ensure that sample_chain's parallel_iterations=1, otherwise results will not be reproducible. 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.

References

• Art B. Owen. Statistically efficient thinning of a Markov chain sampler. Technical Report, 2017.

See also

Other mcmc_functions: mcmc_effective_sample_size(), mcmc_potential_scale_reduction(), mcmc_sample_annealed_importance_chain(), mcmc_sample_halton_sequence()

Examples

# \donttest{
  dims <- 10
  true_stddev <- sqrt(seq(1, 3, length.out = dims))
  likelihood <- tfd_multivariate_normal_diag(scale_diag = true_stddev)

  kernel <- mcmc_hamiltonian_monte_carlo(
    target_log_prob_fn = likelihood$log_prob,
    step_size = 0.5,
    num_leapfrog_steps = 2
  )

  states <- kernel %>% mcmc_sample_chain(
    num_results = 1000,
    num_burnin_steps = 500,
    current_state = rep(0, dims),
    trace_fn = NULL
  )

  sample_mean <- tf$reduce_mean(states, axis = 0L)
  sample_stddev <- tf$sqrt(
    tf$reduce_mean(tf$math$squared_difference(states, sample_mean), axis = 0L))
# }