slice_quantile {qslice}

Quantile Slice Sampler

Description

Single update using a quantile slice sampler of Heiner et al. (2024+).

Usage

slice_quantile(x, log_target, pseudo)

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.

pseudo

List containing two functions specifying the pseudo-target distribution:

ld evaluates the log density for a scalar input, and

q evaluates the quantile (inverse-CDF) function for an input in (0,1).

Value

A list containing three elements:

x is the new state.

u is the value of the CDF of the psuedo-target associated with the returned value (also referred to as psi).

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

References

Heiner, M. J., Johnson, S. B., Christensen, J. R., and Dahl, D. B. (2024+), "Quantile Slice Sampling," arXiv preprint arXiv:###.

Examples

lf <- function(x) dbeta(x, 3, 4, log = TRUE)
pseu <- list(ld = function(x) dbeta(x, shape1 = 1, shape2 = 1, log = TRUE),
             q = function(u) qbeta(u, shape1 = 1, shape2 = 1))
draws <- numeric(10) # set to numeric(1e3) for more complete illustration
nEvaluations <- 0L
for (i in seq.int(2, length(draws))) {
  out <- slice_quantile(draws[i - 1], log_target = lf, pseudo = pseu)
  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)