Effective Sample Size of a multivariate Markov chain.

Description

Calculate the effective sample size of the Markov chain, using the multivariate dependence structure of the process.

Usage

multiESS(x, covmat = NULL, g = NULL)

Arguments

Details

Effective sample size is the size of an iid sample with the same variance as the current sample. ESS is given by

ESS = n |Λ|^{1/p}/ |Σ|^{1/p},

where Λ is the sample covariance matrix for g and Σ is an estimate of the Monte Carlo standard error for g.

Value

The function returns the estimated effective sample size.

See Also

minESS, which calculates the minimum effective samples required for the problem.

ess which calculates univariate effective sample size using a Markov chain and a function g.

Examples

library(mAr)
p <- 3
n <- 1e3
omega <- 5*diag(1,p)

## Making correlation matrix var(1) model
set.seed(100)
foo <- matrix(rnorm(p^2), nrow = p)
foo <- foo %*% t(foo)
phi <- foo / (max(eigen(foo)$values) + 1)
  
out <- as.matrix(mAr.sim(rep(0,p), phi, omega, N = n))

multiESS(out)

Results