slice_elliptical_mv {qslice}

Multivariate Elliptical Slice Sampler

Description

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

Usage

slice_elliptical_mv(x, log_target, mu, Sig, is_chol = FALSE)

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

Numeric vector with the mean of the supporting normal distribution.

Sig

Positive definite covariance matrix. Alternatively, a lower-triangular matrix with the Cholesky factor of the covariance matrix (for faster computation).

is_chol

Logical, is the supplied Sig in Cholesky (lower triangular) format? Default is false.

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[1], 3, 4, log = TRUE) + dbeta(x[2], 5, 3, log = TRUE)
n_iter <- 10 # set to 1e3 for more complete illustration
draws <- matrix(0.3, nrow = n_iter, ncol = 2)
nEvaluations <- 0L
for (i in seq.int(2, n_iter)) {
  out <- slice_elliptical_mv(draws[i - 1,], log_target = lf,
              mu = c(0.5, 0.5), Sig = matrix(c(0.5, 0.25, 0.25, 0.5), nrow = 2))
  draws[i,] <- out$x
  nEvaluations <- nEvaluations + out$nEvaluations
}
nEvaluations / (n_iter - 1)
plot(draws[,1], draws[,2], xlim = c(0, 1))
hist(draws[,1], freq = FALSE); curve(dbeta(x, 3, 4), col = "blue", add = TRUE)
hist(draws[,2], freq = FALSE); curve(dbeta(x, 5, 3), col = "blue", add = TRUE)