leapfrog function

Leapfrog Algorithm for Hamiltonian Monte Carlo

Runs a single iteration of the leapfrog algorithm. Typically called directly from hmc

leapfrog(
  theta_lf,
  r,
  epsilon,
  glogPOSTERIOR,
  Minv,
  constrain,
  lastSTEP = FALSE,
  ...
)

Arguments

• theta_lf: starting parameter vector
• r: starting momentum vector
• epsilon: Step-size parameter for leapfrog
• glogPOSTERIOR: Function to calculate and return the gradient of the log posterior given a vector of values of theta
• Minv: Inverse Mass matrix
• constrain: Optional vector of which parameters in theta accept positive values only. Default is that all parameters accept all real numbers
• lastSTEP: Boolean indicating whether to calculate the last half-step of the momentum update
• ...: Additional parameters passed to glogPOSTERIOR

Returns

List containing two elements: theta.new the ending value of theta and r.new the ending value of the momentum

Examples

set.seed(321)
X <- cbind(1, rnorm(10))
y <- rnorm(10)
p <- runif(3) - 0.5
leapfrog(rep(0,3), p, 0.01, g_linear_posterior,
         diag(3), FALSE, X=X, y=y)

References

Neal, Radford. 2011. MCMC Using Hamiltonian Dynamics. In Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng, 116–62. Chapman; Hall/CRC.