tfp.experimental.mcmc.sample_chain_with_burnin

Implements Markov chain Monte Carlo via repeated TransitionKernel steps.

This function samples from a Markov chain at current_state whose stationary distribution is governed by the supplied TransitionKernel instance (kernel).

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)][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 chain states but no kernel results are traced.

num_results Integer number of Markov chain draws.
current_state Tensor or Python 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).
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 Tensors that is then traced along with the chain state.
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 Python str name prefixed to Ops created by this function. Default value: None (i.e., 'experimental_mcmc_sample_chain_with_burnin').

result A RunKernelResults instance containing information about the sampling run. Main field is trace, the history of outputs of trace_fn. See RunKernelResults for contents of other fields.

References

[1]: Art B. Owen. Statistically efficient thinning of a Markov chain sampler. Technical Report, 2017. http://statweb.stanford.edu/~owen/reports/bestthinning.pdf