### Abstract

The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis-Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.

Original language | English |
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Pages (from-to) | 517-542 |

Number of pages | 26 |

Journal | Journal of the Royal Statistical Society Series C: Applied Statistics |

Volume | 49 |

Issue number | 4 |

Publication status | Published - 2000 |

### Keywords

- Bayesian statistics
- Epidemic data
- Gibbs sampler
- Likelihood approximation
- Markov chain Monte Carlo methods
- Metropolis-hastings algorithm
- Missing data
- Stochastic epidemic models

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## Cite this

*Journal of the Royal Statistical Society Series C: Applied Statistics*,

*49*(4), 517-542.