Compute Monte Carlo standard errors for expectations.
Compute Monte Carlo standard errors for expectations.
mcse(x, size = NULL, g = NULL, r = 3,
method = "bm",
warn = FALSE)x |
a vector of values from a Markov chain. |
size |
represents the batch size in “bm” and the truncation point in “bartlett” and “tukey”. Default is |
g |
a function such that E(g(x)) is the
quantity of interest. The default is |
method |
any of |
r |
the lugsail parameter that converts a lag window into its lugsail equivalent. Larger values of |
warn |
a logical value indicating whether the function should issue a warning if the sample size is too small (less than 1,000). |
mcse returns a list with two elements:
est |
an estimate of E(g(x)). |
se |
the Monte Carlo standard error. |
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).
mcse.mat, which applies mcse to each
column of a matrix or data frame.
mcse.multi, for a multivariate estimate of the Monte Carlo standard error.
mcse.q and mcse.q.mat, which
compute standard errors for quantiles.
# 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")
# Estimate E(x^2) with MCSE using spectral methods.
g = function(x) { x^2 }
mcse(x, g = g, method = "tukey")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.