slice_stepping_out {qslice}

Slice sampler using the Stepping Out and Shrinkage Procedures

Description

Single update for the univariate slice sampler of Neal (2003) using the "stepping out" procedure, followed by the "shrinkage" procedure.

Usage

slice_stepping_out(x, log_target, w, max = Inf)

Arguments

x

The current state (as a numeric scalar).

log_target

A function taking numeric scalar that evaluates the (potentially unnormalized) log-target density, returning a numeric scalar.

w

A numeric scalar tuning the algorithm which gives the typical slice width. This is a main tuning parameter of the algorithm.

max

The maximum number of times to step out. Setting max to zero avoids some evaluations of log_target, but may lead to relatively high autocorrelation if w is too small. If w is too small, setting max to a large value (even Inf) should lead to low autocorrelation at the cost of more evaluations for log_target.

Value

A list with two elements:

x is the new state.

nEvaluations is the number of evaluations of the target function used to obtain the new state.

References

Neal, R. M. (2003), "Slice sampling," The Annals of Statistics, 31, 705-767. doi:10.1214/aos/1056562461

Examples

lf <- function(x) dbeta(x, 3, 4, log = TRUE)
draws <- numeric(10) + 0.5 # set to numeric(1e3) for more complete illustration
nEvaluations <- 0L
for (i in seq.int(2, length(draws))) {
  out <- slice_stepping_out(draws[i - 1], log_target = lf, w = 0.7, max = Inf)
  draws[i] <- out$x
  nEvaluations <- nEvaluations + out$nEvaluations
}
nEvaluations / (length(draws) - 1)
plot(density(draws), xlim = c(0, 1))
curve(exp(lf(x)), 0, 1, col = "blue", add = TRUE)