The Metropolis-Hastings algorithm is a Markov chain Monte Carlo (MCMC) technique which uses a proposal distribution to eventually sample from a target distribution.
mcmc_metropolis_hastings(inner_kernel, seed = NULL, name = NULL)a Monte Carlo sampling kernel
TransitionKernel-like object which has collections$namedtuple
kernel_results and which contains a target_log_prob member and optionally a log_acceptance_correction member.
integer to seed the random number generator.
string prefixed to Ops created by this function. Default value: NULL (i.e., "mh_kernel").
Note: inner_kernel$one_step must return kernel_results as a collections$namedtuple which must:
have a target_log_prob field,
optionally have a log_acceptance_correction field, and,
have only fields which are Tensor-valued.
The Metropolis-Hastings log acceptance-probability is computed as:
log_accept_ratio = (current_kernel_results.target_log_prob
- previous_kernel_results.target_log_prob
+ current_kernel_results.log_acceptance_correction)
If current_kernel_results$log_acceptance_correction does not exist, it is
presumed 0 (i.e., that the proposal distribution is symmetric).
The most common use-case for log_acceptance_correction is in the
Metropolis-Hastings algorithm, i.e.,
accept_prob(x' | x) = p(x') / p(x) (g(x|x') / g(x'|x))
where,
p represents the target distribution,
g represents the proposal (conditional) distribution,
x' is the proposed state, and,
x is current state
The log of the parenthetical term is the log_acceptance_correction.
The log_acceptance_correction may not necessarily correspond to the ratio of
proposal distributions, e.g, log_acceptance_correction has a different
interpretation in Hamiltonian Monte Carlo.
Other mcmc_kernels:
mcmc_dual_averaging_step_size_adaptation(),
mcmc_hamiltonian_monte_carlo(),
mcmc_metropolis_adjusted_langevin_algorithm(),
mcmc_no_u_turn_sampler(),
mcmc_random_walk_metropolis(),
mcmc_replica_exchange_mc(),
mcmc_simple_step_size_adaptation(),
mcmc_slice_sampler(),
mcmc_transformed_transition_kernel(),
mcmc_uncalibrated_hamiltonian_monte_carlo(),
mcmc_uncalibrated_langevin(),
mcmc_uncalibrated_random_walk()