Exact filtering for partially-oberved continuous-time models.

Fearnhead, Paul and Meligkotsidou, Loukia (2004) Exact filtering for partially-oberved continuous-time models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66 (3). pp. 771-789. ISSN 1369-7412

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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: Journal Article
Journal or Publication Title: Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qa
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 9473
Deposited By: Users 810 not found.
Deposited On: 12 Jun 2008 15:22
Refereed?: Yes
Published?: Published
Last Modified: 01 Jan 2020 07:19
URI: https://eprints.lancs.ac.uk/id/eprint/9473

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