## How Many Iterations in the Gibbs Sampler? (1992)

Venue: | In Bayesian Statistics 4 |

Citations: | 96 - 5 self |

### BibTeX

@INPROCEEDINGS{Raftery92howmany,

author = {Adrian E. Raftery and Steven Lewis},

title = {How Many Iterations in the Gibbs Sampler?},

booktitle = {In Bayesian Statistics 4},

year = {1992},

pages = {763--773},

publisher = {Oxford University Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

When the Gibbs sampler is used to estimate posterior distributions (Gelfand and Smith, 1990), the question of how many iterations are required is central to its implementation. When interest focuses on quantiles of functionals of the posterior distribution, we describe an easily-implemented method for determining the total number of iterations required, and also the number of initial iterations that should be discarded to allow for "burn-in". The method uses only the Gibbs iterates themselves, and does not, for example, require external specification of characteristics of the posterior density. Here the method is described for the situation where one long run is generated, but it can also be easily applied if there are several runs from different starting points. It also applies more generally to Markov chain Monte Carlo schemes other than the Gibbs sampler. It can also be used when several quantiles are to be estimated, when the quantities of interest are probabilities rath...

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Citation Context ...drian E. Raftery University of Washington Steven Lewis University of Washington April 10, 1991; revised September 13, 1991 Abstract When the Gibbs sampler is used to estimate posterior distributions (=-=Gelfand and Smith, 1990-=-), the question of how many iterations are required is central to its implementation. When interest focuses on quantiles of functionals of the posterior distribution, we describe an easily-implemented... |

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Citation Context ... them all, even when storage is an issue. An alternative approach to determining the number of iterations starts by viewing the sequence of Gibbs iterates as a standard time series (e.g. Geyer, 1991; =-=Geweke, 1991-=-; Hills and Smith, 1991). If the quantity of interest is the mean of a function of the series, then the variance of such a mean is equal to the spectrum of the corresponding series at zero, which can ... |

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Citation Context ...n when storage is an issue. An alternative approach to determining the number of iterations starts by viewing the sequence of Gibbs iterates as a standard time series (e.g. Geyer, 1991; Geweke, 1991; =-=Hills and Smith, 1991-=-). If the quantity of interest is the mean of a function of the series, then the variance of such a mean is equal to the spectrum of the corresponding series at zero, which can be estimated using stan... |

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