mcmcse (version 1.3-2)

mcse.multi: Multivariate Monte Carlo standard errors for expectations.

Description

Function returns the estimate of the covariance matrix in the Markov Chain CLT using batch means or spectral variance methods (with different lag windows). The function also returns the volume of the resulting ellipsoidal confidence regions.

Usage

mcse.multi(x, method = "bm", size = "sqroot", g = NULL, level = 0.95, large = FALSE)

Arguments

x

a matrix or data frame of Markov chain output. Number of rows is the Monte Carlo sample size.

method

any of ``bm'', ``bartlett'', ``tukey''. ``bm'' represents batch means estimator, ``bartlett'' and ``tukey'' represents the modified-Bartlett window and the Tukey-Hanning windows for the spectral variance estimators.

size

can take character values of ``sqroot'' and ``cuberoot'' or any numeric value between 1 and n. Size represents the batch size in bm and the truncation point in bartlett and tukey. sqroot means size is floor(n^(1/2) and cuberoot means size is floor(n^(1/3)).

g

a function that represents features of interest. g is applied to each row of x and thus g should take a vector input only. If g is NULL, g is set to be identity, which is estimation of the mean of the target density.

level

confidence level of the confidence ellipsoid.

large

if TRUE, returns the volume of the large sample confidence region using a chi square critical value.

Value

A list is returned with the following components,

cov

a covariance matrix estimate.

vol

volume of the confidence ellipsoid to the pth root.

est

estimate of g(x).

nsim

number of rows of the input x.

method

method used to calculate matrix cov.

large

logical of whether a large sample confidence region volume was calculated.

size

value of size used to calculate cov.

References

Vats, D., Flegal, J. M., and, Jones, G. L Multivariate Output Analysis for Markov chain Monte Carlo, arXiv preprint arXiv:1512.07713 (2015).

Vats, D., Flegal, J. M., and, Jones, G. L. (2017+) Strong Consistency of multivariate spectral variance estimators for Markov chain Monte Carlo, Bernoulli.

See Also

mcse.initseq, which computes an initial sequence estimator. mcse, which acts on a vector. mcse.mat, which applies mcse to each column of a matrix or data frame. mcse.q and mcse.q.mat, which compute standard errors for quantiles.

Examples

# NOT RUN {
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))

mcse.bm <- mcse.multi(x = out)
mcse.tuk <- mcse.multi(x = out, method = "tukey")

# If we are only estimating the mean of the first component, 
# and the second moment of the second component

g <- function(x) return(c(x[1], x[2]^2))
mcse <- mcse.multi(x = out, g = g)
# }

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