rsaddle {esaddle}

Simulate random variables from the Extended Empirical Saddlepoint density (ESS)

Description

Simulate random variables from the Extended Empirical Saddlepoint density (ESS), using importance sampling and then resampling according to the importance weights.

Usage

rsaddle(
  n,
  X,
  decay,
  ml = 2,
  multicore = !is.null(cluster),
  cluster = NULL,
  ncores = detectCores() - 1,
  ...
)

Arguments

n

number of simulated vectors.

X

an m by d matrix containing the data.

decay

rate at which the ESS falls back on a normal density. Should be a positive number. See Fasiolo et al. (2016) for details.

ml

n random variables are generated from a Gaussian importance density with covariance matrix ml*cov(X). By default the inflation factor is ml=2.

multicore

if TRUE the ESS densities corresponding the samples will be evaluated in parallel.

cluster

an object of class c("SOCKcluster", "cluster"). This allowes the user to pass her own cluster, which will be used if multicore == TRUE. The user has to remember to stop the cluster.

ncores

number of cores to be used.

...

additional arguments to be passed to dsaddle.

Details

Notice that, while importance sampling is used, the output is a matrix of unweighted samples, obtained by resampling with probabilities proportional to the importance weights.

Value

An n by d matrix containing the simulated vectors.

Author(s)

Matteo Fasiolo <[e-mail]>.

References

Fasiolo, M., Wood, S. N., Hartig, F. and Bravington, M. V. (2016). An Extended Empirical Saddlepoint Approximation for Intractable Likelihoods. ArXiv http://arxiv.org/abs/1601.01849.

Examples

# Simulate bivariate data, where each marginal distribution is Exp(2)
X <- matrix(rexp(2 * 1e3), 1e3, 2)

# Simulate bivariate data from a saddlepoint fitted to X
Z <- rsaddle(1000, X, decay = 0.5)

# Look at first marginal distribution
hist( Z[ , 1] )