Effective Sample Size of a multivariate Markov chain as described in Vats et al. (2015).
Calculate the effective sample size of the Markov chain, using the multivariate dependence structure of the process.
multiESS(x, covmat = NULL, g = NULL, ...)
x |
a matrix or data frame of Markov chain output. Number of rows is the Monte Carlo sample size. |
covmat |
optional matrix estimate obtained using |
g |
a function that represents features of interest. g is applied to each row of |
... |
arguments for |
.
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.
The function returns the estimated effective sample size.
Vats, D., Flegal, J. M., and, Jones, G. L Multivariate Output Analysis for Markov chain Monte Carlo, arXiv preprint arXiv:1512.07713 (2015).
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.
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)
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