hmc_neal_2010: Hamiltonian Monte Carlo (HMC) Implementation

In catalytic: Tools for Applying Catalytic Priors in Statistical Modeling

Hamiltonian Monte Carlo (HMC) Implementation

Description

This function implements the Hamiltonian Monte Carlo algorithm as described by Radford M. Neal (2010) in "MCMC using Hamiltonian dynamics", which is a part of the Handbook of Markov Chain Monte Carlo. The method uses Hamiltonian dynamics to propose new positions and then applies the Metropolis criterion to decide whether to accept or reject the new position.

Usage

hmc_neal_2010(
  neg_log_den_func,
  neg_log_den_grad_func,
  leapfrog_stepsize,
  leapfrog_step,
  current_pos
)

Arguments

neg_log_den_func	A function that evaluates the negative log of the density (potential energy) of the distribution to be sampled, including any constants.
neg_log_den_grad_func	A function that computes the gradient of neg_log_den_func.
leapfrog_stepsize	A numeric value specifying the step size for the leapfrog integration method.
leapfrog_step	A numeric value specifying the number of leapfrog steps to take to propose a new state.
current_pos	A numeric vector representing the current position (state) of the system.

Details

This function was written for illustrative purposes. More elaborate on Radford M. Neal's personal webpage (http://www.cs.utoronto.ca/~radford/).

Value

A list containing the following elements:

• position: The position of the system after the leapfrog steps, which is the proposed new position if accepted, or the current position if rejected.

• potential_energy: The potential energy of the proposed position.

• accepted: A logical value indicating whether the proposal was accepted (TRUE) or rejected (FALSE).

References

Neal, R. M. (2012). MCMC using Hamiltonian dynamics. arXiv:1206.1901. Available at: https://arxiv.org/pdf/1206.1901

catalytic documentation built on April 4, 2025, 5:51 a.m.