slice_elliptical {qslice}

Univariate Elliptical Slice Sampler

Description

Algorithm 1 of Nishihara et al. (2014) of the elliptical slice sampler of Murray et al. (2010).

Usage

slice_elliptical(x, log_target, mu, sigma)

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.

Value

A list with two elements:

x is the new state.

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

References

Murray, I., Adams, R., and MacKay, D., (2010), "Elliptical Slice Sampling," in Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, JMLR Workshop and Conference Proceedings. https://proceedings.mlr.press/v9/murray10a

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_elliptical(draws[i - 1], log_target = lf, mu = 0.5, sigma = 1)
  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)