mcmcse (version 0.1)

mcmcse-package: Monte Carlo standard errors for MCMC

Description

Tools for calculating Monte Carlo standard errors (MCSE) in Markov chain Monte Carlo (MCMC) settings. This package considers standard errors for expectation and quantile estimators.

Details

ll{ Package: mcse Type: Package Version: 0.1 Date: 2012-05-14 License: GPL LazyLoad: yes }

References

Flegal, J. M. (2012). Applicability of subsampling bootstrap methods in {M}arkov chain {M}onte {C}arlo. In Wozniakowski, H. and Plaskota, L., editors, Monte Carlo and Quasi-Monte Carlo Methods 2010 (to appear). Springer-Verlag.

Flegal, J. M. and Jones, G. L. (2010). Batch means and spectral variance estimators in {M}arkov chain {M}onte {C}arlo. The Annals of Statistics, 38:1034--1070.

Flegal, J. M. and Jones, G. L. (2011). Implementing {M}arkov chain {M}onte {C}arlo: Estimating with confidence. In Brooks, S., Gelman, A., Jones, G., and Meng, X., editors, Handbook of {M}arkov Chain {M}onte {C}arlo, pages 175--197. Chapman & Hall/CRC Press.

Flegal, J. M., Jones, G. L., and Neath, R. (2012). Quantile Estimation via {M}arkov chain {M}onte {C}arlo. University of California, Riverside, Technical Report.

Jones, G. L., Haran, M., Caffo, B. S., and Neath, R. (2006). Fixed-width output analysis for {M}arkov chain {M}onte {C}arlo. Journal of the American Statistical Association, 101:1537--1547.

Examples

# Creates 10000 iterations in an AR(1) Markov chain with rho = .9
p <- 10000
tau <- 1
mc <- double(p)
mc[1] <- 2
for(i in 1:(p-1)){
mc[(i+1)] <- .9 * mc[i] + rnorm(1, 0, tau)
}

# Estimates the mean, .1 quantile and .9 quantile with MCSE using BM
mcse(mc)
mcse.q(mc, .1)
mcse.q(mc, .9)

# Estimates the mean, .1 quantile and .9 quantile with MCSE using OBM
mcse(mc, meth="OBM")
mcse.q(mc, .1, meth="OBM")
mcse.q(mc, .9, meth="OBM")

# Estimates E(x^2) with MCSE using spectral methods
g.fun <- function(x){x^2}
mcse(mc, g=g.fun, meth="TukeyHanning")