slice_genelliptical {qslice}

Generalized Elliptical Slice Sampler (univariate)

Description

Single update using the generalized elliptical slice sampler of Nishihara et al. (2014).

Usage

slice_genelliptical(x, log_target, mu, sigma, df)

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.

mu

A numeric scalar with the mean of the supporting normal distribution.

sigma

A numeric scalar with the standard deviation of the supporting normal distribution.

df

Degrees of freedom of Student t pseudo-target.

Value

A list contains two elements:

x is the new state.

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

References

Nishihara, R., Murray, I., and Adams, R. P. (2014), "Parallel MCMC with Generalized Elliptical Slice Sampling," Journal of Machine Learning Research, 15, 2087-2112. https://jmlr.org/papers/v15/nishihara14a.html

Examples

lf <- function(x) dbeta(x, 3, 4, log = TRUE)
draws <- numeric(10) # set to numeric(1e3) for more complete illustration
nEvaluations <- 0L
for (i in seq.int(2, length(draws))) {
  out <- slice_genelliptical(draws[i - 1], log_target = lf,
                                      mu = 0.5, sigma = 1, df = 5)
  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)