Fearnhead, Paul and Meligkotsidou, Loukia (2004) *Exact filtering for partially-oberved continuous-time models.* Journal of the Royal Statistical Society: Series B, 66 (3). pp. 771-789. ISSN 1467-9868

## Abstract

Summary. The forward–backward algorithm is an exact filtering algorithm which can efficiently calculate likelihoods, and which can be used to simulate from posterior distributions. Using a simple result which relates gamma random variables with different rates, we show how the forward–backward algorithm can be used to calculate the distribution of a sum of gamma random variables, and to simulate from their joint distribution given their sum. One application is to calculating the density of the time of a specific event in a Markov process, as this time is the sum of exponentially distributed interevent times. This enables us to apply the forward–backward algorithm to a range of new problems. We demonstrate our method on three problems: calculating likelihoods and simulating allele frequencies under a non-neutral population genetic model, analysing a stochastic epidemic model and simulating speciation times in phylogenetics.

Item Type: | Article |
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Journal or Publication Title: | Journal of the Royal Statistical Society: Series B |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 9473 |

Deposited By: | Mrs Yaling Zhang |

Deposited On: | 12 Jun 2008 16:22 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 09 Oct 2013 15:43 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/9473 |

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