Perform consistent batch means estimation on a vector of values from a Markov chain.

Description

Perform consistent batch means estimation on a vector of values from a Markov chain.

Usage

bm(x, size = "sqroot", warn = FALSE)

Arguments

Value

bm returns a list with two elements:

References

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.

The following article is less technical and contains a direct comparison to the Gelman-Rubin diagnostic.

Flegal, J. M., Haran, M. and Jones, G. L. (2008) Markov chain Monte Carlo: Can we trust the third significant figure? Statistical Science, 23, 250–260.

See Also

bmmat, which applies bm to each column of a matrix or data frame.

Examples

# Simulate a sample path of length 10,000 for an AR(1) chain with rho equal to 0.7.

X = numeric(10000)
X[1] = 1
for (i in 1:9999)
    X[i + 1] = 0.7 * X[i] + rnorm(1)

# Estimate the mean and MCSE.

bm(X)

Apply bm to each column of a matrix or data frame of MCMC samples.

Description

Apply bm to each column of a matrix or data frame of MCMC samples.

Usage

bmmat(x)

Arguments

Value

bmmat returns a matrix with ncol(x) rows and two columns. The row names of the matrix are the same as the column names of x. The column names of the matrix are “est” and “se”. The jth row of the matrix contains the result of applying bm to the jth column of x.

See Also

bm, which performs consistent batch means estimation for a vector.

Estimate effective sample size (ESS) as described in Kass et al. (1998) and Robert and Casella (2004; p. 500).

Description

Estimate effective sample size (ESS) as described in Kass et al. (1998) and Robert and Casella (2004; p. 500).

Usage

ess(x, imse = TRUE, verbose = FALSE)

Arguments

Details

ESS is the size of an iid sample with the same variance as the current sample. ESS is given by

\mbox{ESS}=T/\eta,

where

\eta=1+2\sum \mbox{all lag autocorrelations}.

Value

The function returns the estimated effective sample size.

References

Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. (1998) Markov chain Monte Carlo in practice: A roundtable discussion. The American Statistician, 52, 93–100.

Robert, C. P. and Casella, G. (2004) Monte Carlo Statistical Methods. New York: Springer.

Geyer, C. J. (1992) Practical Markov chain Monte Carlo. Statistical Science, 7, 473–483.

Create a plot that shows how Monte Carlo estimates change with increasing sample size.

Description

Create a plot that shows how Monte Carlo estimates change with increasing sample size.

Usage

estvssamp(x, fun = mean, main = "Estimate vs Sample Size", add = FALSE,
  ...)

Arguments

Value

NULL

Examples

# Simulate a sample path of length 10,000 for an AR(1) chain with rho equal to 0.7.

X = numeric(10000)
X[1] = 1
for (i in 1:9999)
    X[i + 1] = 0.7 * X[i] + rnorm(1)

# Plot MC estimates versus sample size.

estvssamp(X)