Runs one step of the slice sampler using a hit and run approach

Slice Sampling is a Markov Chain Monte Carlo (MCMC) algorithm based, as stated by Neal (2003), on the observation that "...one can sample from a distribution by sampling uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternately uniform sampling in the vertical direction with uniform sampling from the horizontal slice defined by the current vertical position, or more generally, with some update that leaves the uniform distribution over this slice invariant". Mathematical details and derivations can be found in Neal (2003). The one dimensional slice sampler is extended to n-dimensions through use of a hit-and-run approach: choose a random direction in n-dimensional space and take a step, as determined by the one-dimensional slice sampling algorithm, along that direction (Belisle at al. 1993).

mcmc_slice_sampler(
  target_log_prob_fn,
  step_size,
  max_doublings,
  seed = NULL,
  name = NULL
)

Arguments

target_log_prob_fn	Function which takes an argument like current_state (if it's a list current_state will be unpacked) and returns its (possibly unnormalized) log-density under the target distribution.
step_size	Tensor or list of Tensors representing the step size for the leapfrog integrator. Must broadcast with the shape of current_state. Larger step sizes lead to faster progress, but too-large step sizes make rejection exponentially more likely. When possible, it's often helpful to match per-variable step sizes to the standard deviations of the target distribution in each variable.
max_doublings	Scalar positive int32 tf$Tensor. The maximum number of doublings to consider.
seed	integer to seed the random number generator.
name	string prefixed to Ops created by this function. Default value: NULL (i.e., 'slice_sampler_kernel').

Value

list of next_state (Tensor or Python list of Tensors representing the state(s) of the Markov chain(s) at each result step. Has same shape as and current_state.) and kernel_results (collections$namedtuple of internal calculations used to 'advance the chain).

Details

The one_step function can update multiple chains in parallel. It assumes that all leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(*current_state) should sum log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, current_state[0, :] could have a different target distribution from current_state[1, :]. These semantics are governed by target_log_prob_fn(*current_state). (The number of independent chains is tf$size(target_log_prob_fn(*current_state)).)

Note that the sampler only supports states where all components have a common dtype.

References

• Radford M. Neal. Slice Sampling. The Annals of Statistics. 2003, Vol 31, No. 3 , 705-767.

• C.J.P. Belisle, H.E. Romeijn, R.L. Smith. Hit-and-run algorithms for generating multivariate distributions. Math. Oper. Res., 18(1993), 225-266.

See also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_random_walk_metropolis(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()