slice_genelliptical_mv {qslice}

Generalized Elliptical Slice Sampler (Multivariate)

Description

Generalized Elliptical Slice Sampler, Algorithm 2 of Nishihara et al. (2014)

Usage

slice_genelliptical_mv(x, log_target, mu, Sig, df, 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).

df

Degrees of freedom of Student t pseudo-target.

is_chol

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

Value

A list contains two elements: x is the new state and 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[1], 3, 4, log = TRUE) + dbeta(x[2], 5, 3, log = TRUE)
n_iter <- 10 # set to 1e4 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_genelliptical_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),
              df = 5)
  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)