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

Value

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

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.

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)

#> $theta.new
#> [1]  0.003425262 -0.002263951 -0.000395666
#> 
#> $r.new
#> [1]  0.36441092 -0.22888346 -0.03657306
#>