Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that takes a series of gradient-informed steps to produce a Metropolis proposal. This class implements one random HMC step from a given current_state. Mathematical details and derivations can be found in Neal (2011).

mcmc_hamiltonian_monte_carlo(
target_log_prob_fn,
step_size,
num_leapfrog_steps,
)
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. 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. Integer number of steps to run the leapfrog integrator for. Total progress per HMC step is roughly proportional to step_size * num_leapfrog_steps. logical indicating that the proposed new state be run through tf$stop_gradient. This is particularly useful when combining optimization over samples from the HMC chain. Default value: FALSE (i.e., do not apply stop_gradient). Function taking current step_size (typically a tf$Variable) and kernel_results (typically collections$namedtuple) and returns updated step_size (Tensors). Default value: NULL (i.e., do not update step_size automatically). integer to seed the random number generator. If TRUE, then step_size and num_leapfrog_steps are written to and read from eponymous fields in the kernel results objects returned from one_step and bootstrap_results. This allows wrapper kernels to adjust those parameters on the fly. This is incompatible with step_size_update_fn, which must be set to NULL. string prefixed to Ops created by this function. Default value: NULL (i.e., 'hmc_kernel'). ## Value a Monte Carlo sampling kernel ## Details The one_step function can update multiple chains in parallel. It assumes that all leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(current_state) should sum log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, current_state[0, :] could have a different target distribution from current_state[1, :]. These semantics are governed by target_log_prob_fn(current_state). (The number of independent chains is tf$size(target_log_prob_fn(current_state)).)
Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), 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_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()