pseudo_condseq: Sequence of conditional pseudo-targets from a realization

In qslice: Implementations of Various Slice Samplers

Sequence of conditional pseudo-targets from a realization

Description

Given a realization of a random vector, generate the corresponding sequence of conditional pseudo-targets (Heiner et al., 2026+). The pseudo-target is specified as a sequence of growing conditional distributions.

Usage

pseudo_condseq(x, pseudo_init, loc_fn, sc_fn, lb, ub)

Arguments

x	A numeric vector (length at least two) giving the realization of the random vector on its original scale.
pseudo_init	A list output from pseudo_list describing the marginal pseudo-target for x[1]. All subsequent pseudo-targets will resemble pseudo_init with exception of different location and scale parameters.
loc_fn	A function that specifies the location of a conditional pseudo-target given the elements in x that precede it.
sc_fn	A function that specifies the scale of a conditional pseudo-target given the elements in x that precede it
lb	A numeric vector (same length as x) specifying the lower bound of support for each conditional pseudo-target.
ub	A numeric vector (same length as x) specifying the upper bound of support for each conditional pseudo-target.

Details

See the documentation for slice_quantile_mv_seq for examples.

Value

A list containing a sequence of pseudo-targets, each from pseudo_list.

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

# Funnel distribution from Neal (2003).
K <- 10
n_iter <- 50 # MCMC iterations; set to 10e3 for more complete illustration
n <- 100 # number of iid samples from the target; set to 10e3 for more complete illustration
Y <- matrix(NA, nrow = n, ncol = K) # iid samples from the target
Y[, 1] <- rnorm(n, 0.0, 3.0)
for (i in 1:n) {
  Y[i, 2:K] <- rnorm(K - 1, 0.0, exp(0.5 * Y[i, 1]))
}
ltarget <- function(x) {
  dnorm(x[1], 0.0, 3.0, log = TRUE) +
    sum(dnorm(x[2:K], 0.0, exp(0.5 * x[1]), log = TRUE))
}
pseudo_control <- list(
  loc_fn = function(x) {
    0.0
  },
  sc_fn = function(x) {
    if (is.null(x)) {
      out <- 3.0
    } else {
      out <- exp(0.5 * x[1])
    }
    out
  },
  pseudo_init = pseudo_list(
    family = "t",
    params = list(loc = 0.0, sc = 3.0, df = 20),
    lb = -Inf,
    ub = Inf
  ),
  lb = rep(-Inf, K),
  ub = rep(Inf, K)
)
x0 <- runif(K)
draws <- matrix(rep(x0, n_iter + 1), nrow = n_iter + 1, byrow = TRUE)
draws_u <- matrix(rep(x0, n_iter), nrow = n_iter, byrow = TRUE)
n_eval <- 0
for (i in 2:(n_iter + 1)) {
  tmp <- slice_quantile_mv_seq(
    draws[i - 1, ],
    log_target = ltarget,
    pseudo_control = pseudo_control
  )
  draws[i, ] <- tmp$x
  draws_u[i - 1, ] <- tmp$u
  n_eval <- n_eval + tmp$nEvaluations
}
# (es <- coda::effectiveSize(coda::as.mcmc(draws)))
# mean(es)
n_eval / n_iter
sapply(1:K, function(k) {
  utility_shrinkslice(u = draws_u[, k], utility_type = "AUC")
})
hist(draws_u[, 1])
plot(draws[, 1], draws[, 2])
points(Y[, 1], Y[, 2], col = "blue", cex = 0.5)

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