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Last data update: 2014.03.03

R: Compute Monte Carlo standard errors for expectations.

mcse	R Documentation

Compute Monte Carlo standard errors for expectations.

Description

Compute Monte Carlo standard errors for expectations.

Usage

  mcse(x, size = "sqroot", g = NULL,
    method = c("bm", "obm", "tukey", "bartlett"),
    warn = FALSE)

Arguments

`x`	a vector of values from a Markov chain.
`size`	the batch size. The default value is “`sqroot`”, which uses the square root of the sample size. “`cuberoot`” will cause the function to use the cube root of the sample size. A numeric value may be provided if neither “`sqroot`” nor “`cuberoot`” is satisfactory.
`g`	a function such that E(g(x)) is the quantity of interest. The default is `NULL`, which causes the identity function to be used.
`method`	the method used to compute the standard error. This is one of “`bm`” (batch means, the default), “`obm`” (overlapping batch means), “`tukey`” (spectral variance method with a Tukey-Hanning window), or “`bartlett`” (spectral variance method with a Bartlett window).
`warn`	a logical value indicating whether the function should issue a warning if the sample size is too small (less than 1,000).

Value

mcse returns a list with two elements:

`est`	an estimate of E(g(x)).
`se`	the Monte Carlo standard error.

References

Flegal, J. M. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. 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 Markov chain Monte Carlo. The Annals of Statistics, 38, 1034–1070.

Flegal, J. M. and Jones, G. L. (2011) Implementing Markov chain Monte Carlo: Estimating with confidence. In Brooks, S., Gelman, A., Jones, G. L., and Meng, X., editors, Handbook of Markov Chain Monte Carlo, pages 175–197. Chapman & Hall/CRC Press.

Flegal, J. M., Jones, G. L., and Neath, R. (2012) Markov chain Monte Carlo estimation of quantiles. University of California, Riverside, Technical Report.

Gong, L., and Flegal, J. M. A practical sequential stopping rule for high-dimensional Markov chain Monte Carlo. Journal of Computational and Graphical Statistics (to appear).

Jones, G. L., Haran, M., Caffo, B. S. and Neath, R. (2006) Fixed-width output analysis for Markov chain Monte Carlo. Journal of the American Statistical Association, 101, 1537–1547.

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

Examples

# Create 10,000 iterations of an AR(1) Markov chain with rho = 0.9.

n = 10000
x = double(n)
x[1] = 2
for (i in 1:(n - 1))
    x[i + 1] = 0.9 * x[i] + rnorm(1)

# Estimate the mean, 0.1 quantile, and 0.9 quantile with MCSEs using batch means.

mcse(x)
mcse.q(x, 0.1)
mcse.q(x, 0.9)

# Estimate the mean, 0.1 quantile, and 0.9 quantile with MCSEs using overlapping batch means.

mcse(x, method = "obm")
mcse.q(x, 0.1, method = "obm")
mcse.q(x, 0.9, method = "obm")

# Estimate E(x^2) with MCSE using spectral methods.

g = function(x) { x^2 }
mcse(x, g = g, method = "tukey")

Compute Monte Carlo standard errors for expectations.

Description

Usage

Arguments

Value

References

See Also

Examples

Results