Description Usage Arguments Value References See Also Examples

Compute Monte Carlo standard errors for expectations.

1 |

`x` |
a vector of values from a Markov chain of length n. |

`size` |
represents the batch size in “ |

`g` |
a function such that |

`r` |
The lugsail parameters ( |

`method` |
any 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 three elements:

`est` |
an estimate of |

`se` |
the Monte Carlo standard error. |

`nsim` |
The number of samples in the input Markov chain. |

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*, pp. 363-372. 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.

Doss, C. R., Flegal, J. M., Jones, G. L., and Neath, R. C. (2014). Markov chain Monte Carlo estimation of quantiles. *Electronic Journal of Statistics*, **8**, 2448-2478.
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**, 1537–154.

`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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
## Bivariate Normal with mean (mu1, mu2) and covariance sigma
n <- 1e3
mu = c(2, 50)
sigma = matrix(c(1, 0.5, 0.5, 1), nrow = 2)
out = BVN_Gibbs(n, mu, sigma)
x = out[,1]
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")
``` |

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