tfp.substrates.numpy.experimental.mcmc.sample_sequential_monte_carlo

Runs Sequential Monte Carlo to sample from the posterior distribution.

This function uses an MCMC transition operator (e.g., Hamiltonian Monte Carlo) to sample from a series of distributions that slowly interpolates between an initial 'prior' distribution:

exp(prior_log_prob_fn(x))

and the target 'posterior' distribution:

exp(prior_log_prob_fn(x) + target_log_prob_fn(x)),

by mutating a collection of MC samples (i.e., particles). The approach is also known as Particle Filter in some literature. The current implemenetation is largely based on Del Moral et al [1], which adapts the tempering sequence adaptively (base on the effective sample size) and the scaling of the mutation kernel (base on the sample covariance of the particles) at each stage.

prior_log_prob_fn Python callable that returns the log density of the prior distribution.
likelihood_log_prob_fn Python callable which takes an argument like current_state (or *current_state if it's a list) and returns its (possibly unnormalized) log-density under the likelihood distribution.
current_state Nested structure of Tensors, each of shape concat([[num_particles, b1, ..., bN], latent_part_event_shape]), where b1, ..., bN are optional batch dimensions. Each batch represents an independent SMC run.
min_num_steps The minimal number of kernel transition steps in one mutation of the MC samples.
max_num_steps The maximum number of kernel transition steps in one mutation of the MC samples. Note that the actual number of steps in one mutation is tuned during sampling and likely lower than the max_num_step.
max_stage Integer number of the stage for increasing the temperature from 0 to 1.
make_kernel_fn Python callable which returns a TransitionKernel-like object. Must take one argument representing the TransitionKernel's target_log_prob_fn. The target_log_prob_fn argument represents the TransitionKernel's target log distribution. Note: sample_sequential_monte_carlo creates a new target_log_prob_fn which is an interpolation between the supplied target_log_prob_fn and proposal_log_prob_fn; it is this interpolated function which is used as an argument to make_kernel_fn.
tuning_fn Python callable which takes the number of steps, the log scaling, and the log acceptance ratio from the last mutation and output the number of steps and log scaling for the next mutation.
make_tempered_target_log_prob_fn Python callable that takes the prior_log_prob_fn, likelihood_log_prob_fn, and inverse_temperatures and creates a target_log_prob_fn callable that pass to make_kernel_fn.
resample_fn Python callable to generate the indices of resampled particles, given their weights. Generally, one of tfp.experimental.mcmc.resample_independent or tfp.experimental.mcmc.resample_systematic, or any function with the same signature. Default value: tfp.experimental.mcmc.resample_systematic.
ess_threshold_ratio Target ratio for effective sample size.
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 Python integer or TFP seedstream to seed the random number generator.
name Python str name prefixed to Ops created by this function. Default value: None (i.e., 'sample_sequential_monte_carlo').

n_stage Number of the mutation stage SMC ran.
final_state Tensor or Python list of Tensors representing the final state(s) of the Markov chain(s). The output are the posterior samples.
final_kernel_results collections.namedtuple of internal calculations used to advance the chain.

References

[1] Del Moral, Pierre, Arnaud Doucet, and Ajay Jasra. An adaptive sequential Monte Carlo method for approximate Bayesian computation. Statistics and Computing, 22.5(1009-1020), 2012.