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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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:
Journal Article
Journal or Publication Title:
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
?? statistics and probabilitystatistics, probability and uncertaintyqa mathematics ??
ID Code:
9473
Deposited By:
Users 810 not found.
Deposited On:
12 Jun 2008 15:22
Refereed?:
Yes
Published?:
Published
Last Modified:
15 Jul 2024 11:40