Sahu, Sujit K. and Roberts, Gareth O. (1999) *On convergence of the EM algorithm and the Gibbs sampler.* Statistics and Computing, 9 (1). pp. 55-64. ISSN 0960-3174

## Abstract

In this article we investigate the relationship between the EM algorithm and the Gibbs sampler. We show that the approximate rate of convergence of the Gibbs sampler by Gaussian approximation is equal to that of the corresponding EM-type algorithm. This helps in implementing either of the algorithms as improvement strategies for one algorithm can be directly transported to the other. In particular, by running the EM algorithm we know approximately how many iterations are needed for convergence of the Gibbs sampler. We also obtain a result that under certain conditions, the EM algorithm used for finding the maximum likelihood estimates can be slower to converge than the corresponding Gibbs sampler for Bayesian inference. We illustrate our results in a number of realistic examples all based on the generalized linear mixed models.

Item Type: | Article |
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Journal or Publication Title: | Statistics and Computing |

Uncontrolled Keywords: | Gaussian distribution - Generalized linear mixed models - Markov chain Monte Carlo - Parameterization - Rate of convergence |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Lancaster Environment Centre |

ID Code: | 19428 |

Deposited By: | ep_ss_importer |

Deposited On: | 13 Nov 2008 12:31 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 13 Jan 2016 11:00 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19428 |

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