pseudo_condseq_XfromU: Inverse transform from sequence of conditional pseudo-targets

In qslice: Implementations of Various Slice Samplers

Inverse transform from sequence of conditional pseudo-targets

Description

Given a vector from the unit hypercube, map to the original (back-transformed) vector using a sequence of conditional pseudo-target inverse CDFs. The pseudo-target is specified as a sequence of growing conditional distributions.

Usage

pseudo_condseq_XfromU(
  u,
  pseudo_init,
  loc_fn,
  sc_fn,
  lb,
  ub,
  diagnostics = NULL
)

Arguments

u	A numeric vector (length at least two) of values strictly between 0 and 1.
pseudo_init	A list output from pseudo_list describing the marginal pseudo-target for x[1].
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 u) specifying the lower bound of support for each conditional pseudo-target.
ub	A numeric vector (same length as u) specifying the upper bound of support for each conditional pseudo-target.
diagnostics	Logical, indicating whether the function 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.

Details

See the documentation for slice_quantile_mv_seq for examples.

Value

A list containing x obtained from the sequence of inverse CDFs, and pseudo_seq, a list of the corresponding sequential pseudo-targets output from pseudo_list.

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.