## Abstract

The Stochastic EM algorithm is a Monte Carlo method for approximating the regular EM algorithm in missing data situations where the E step is intractable. It produces a stationary Markov chain iterative sequence where each iteration is the result of applying complete data maximum likelihood estimation to a single simulation of the complete data conditional on the observed data. Analogously to other Markov chain Monte Carlo methods, the final estimate is the mean of the iterative sequence after a burn-in period. We consider a case study of the application of the Stochastic EM algorithm for censored mixed models, a computationally challenging context. The Stochastic EM algorithm is particularly simple to apply to either linear or non-linear mixed models with censoring. All that is required is a routine to simulate censored multivariate normal observations, and a routine to fit the desired uncensored mixed model. An application is presented involving repeated measures of HIV viral load subject to censoring caused by a lower detection limit of the assay. It is found that crude methods ignoring the censoring are biased compared to results from the Stochastic EM algorithm.

Original language | English |
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Title of host publication | Monte Carlo and Quasi-Monte Carlo Methods 2012 |

Editors | Josef Dick, Frances Y. Kuo, Gareth W. Peters, Ian H. Sloan |

Place of Publication | Heidelberg |

Publisher | Springer, Springer Nature |

Pages | 553-567 |

Number of pages | 15 |

Volume | 65 |

ISBN (Electronic) | 9783642410956 |

ISBN (Print) | 9783642410949 |

DOIs | |

Publication status | Published - 2013 |

Event | 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012 - Sydney, NSW, Australia Duration: 13 Feb 2012 → 17 Feb 2012 |

### Other

Other | 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012 |
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Country/Territory | Australia |

City | Sydney, NSW |

Period | 13/02/12 → 17/02/12 |