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