slice_quantile_mv: Multivariate Quantile Slice Sampler

In qslice: Implementations of Various Slice Samplers

Multivariate Quantile Slice Sampler

Description

Quantile slice sampler for a random vector (Heiner et al., 2026+). The pseudo-target is specified through independent univariate distributions.

Usage

slice_quantile_mv(x, log_target, pseudo, diagnostics = NULL)

Arguments

x	The current state (as a numeric vector).
log_target	A function taking numeric vector that evaluates the log-target density, returning a numeric scalar.
pseudo	List of length equal to the number of dimensions in x. Each element is itself a list that specifies the pseudo-target for the corresponding dimension with functions ld that evaluates the log density, p that evaluates the CDF, and q that evaluates the quantile (inverse-CDF) function.
diagnostics	Logical, indicating whether the sampler should be run in diagnostic mode for informative error handling. When diagnostics is NULL, it is reset to match the value of getOption("qslice.diagnostics") which defaults to FALSE if the option is not set. Default for diagnostics is NULL.

Value

A list containing three elements: "x" is the new state, "u" is the vector of values of the pseudo-target CDFs associated with the returned value, and "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. (2026+), "Quantile Slice Sampling," arXiv preprint arXiv:2407.12608 \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.48550/arXiv.2407.12608")}

Examples

lf <- function(x) dbeta(x[1], 3, 4, log = TRUE) + dbeta(x[2], 5, 3, log = TRUE)
ps_shsc <- list(c(2, 2), c(2, 1))
ps <- list(
  list(ld = function(x) dbeta(x, ps_shsc[[1]][1], ps_shsc[[1]][2], log = TRUE),
       p = function(x) pbeta(x, ps_shsc[[1]][1], ps_shsc[[1]][2]),
       q = function(x) qbeta(x, ps_shsc[[1]][1], ps_shsc[[1]][2]) ),
  list(ld = function(x) dbeta(x, ps_shsc[[2]][1], ps_shsc[[2]][2], log = TRUE),
       p = function(x) pbeta(x, ps_shsc[[2]][1], ps_shsc[[2]][2]),
       q = function(x) qbeta(x, ps_shsc[[2]][1], ps_shsc[[2]][2]) )
  )
n_iter <- 10 # set to 1e4 for more complete illustration
draws <- matrix(0.2, nrow = n_iter, ncol = 2)
draws_u <- draws
draws_u[1,] <- sapply(1:length(ps), function(k) ps[[k]]$p(draws[1,k]))
nEvaluations <- 0L
for (i in seq.int(2, n_iter)) {
  out <- slice_quantile_mv(draws[i - 1, ], log_target = lf, pseudo = ps)
  draws[i,] <- out$x
  draws_u[i,] <- out$u
  nEvaluations <- nEvaluations + out$nEvaluations
  cat(i, '\r')
}
nEvaluations / (nrow(draws) - 1)
plot(draws[,1], draws[,2], xlim = c(0, 1))
hist(draws[,1], freq = FALSE); curve(dbeta(x, 3, 4), col = "blue", add = TRUE)
hist(draws[,2], freq = FALSE); curve(dbeta(x, 5, 3), col = "blue", add = TRUE)
plot(draws_u[,1], draws_u[,2], xlim = c(0, 1))
utility_shrinkslice(u = draws_u[,1], nbins = 30, type = "samples",
plot = TRUE, utility_type = "AUC")
utility_shrinkslice(u = draws_u[,2], nbins = 30, type = "samples",
plot = TRUE, utility_type = "AUC")

qslice documentation built on Oct. 22, 2026, 1:06 a.m.