pseudo_condseq {qslice}

Sequence of conditional pseudo-targets from a realization

Description

Given a realization of a random vector, generate a the corresponding sequence of conditional pseudo-target inverse CDFs (Heiner et al., 2024+). 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 of values between 0 and 1.

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. (2024+), "Quantile Slice Sampling," arXiv preprint arXiv:###

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, degf = 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) auc(u = draws_u[,k]))
hist(draws_u[,1])
plot(draws[,1], draws[,2])
points(Y[,1], Y[,2], col = "blue", cex = 0.5)