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Fitting the Bartlett-Lewis rainfall model using approximate Bayesian computation

Aryal, Nanda and Jones, Owen 2020. Fitting the Bartlett-Lewis rainfall model using approximate Bayesian computation. Mathematics and Computers in Simulation 175 , pp. 153-163. 10.1016/j.matcom.2019.10.018

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The Bartlett–Lewis (BL) rainfall model is a stochastic model for the rainfall at a single point in space, constructed using a cluster point process. The cluster process is constructed by taking a primary/parent process, called the storm arrival process in our context, and then attaching to each storm point a finite secondary/daughter point process, called a cell arrival process. To each cell arrival point we then attach a rain cell, with an associated rainfall duration and intensity. The total rainfall at time is then the sum of the intensities from all active cells at that time. Because it has an intractable likelihood function, in the past the BL model has been fitted using the Generalised Method of Moments (GMM). The purpose of this paper is to show that Approximate Bayesian Computation (ABC) can also be used to fit this model, and moreover that it gives a better fit than GMM. GMM fitting matches theoretical and observed moments of the process, and thus is restricted to moments for which you have an analytic expression. ABC fitting compares the observed process to simulations, and thus places no restrictions on the statistics used to compare them. The penalty we pay for this increased flexibility is an increase in computational time.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0378-4754
Date of First Compliant Deposit: 29 January 2020
Date of Acceptance: 26 October 2019
Last Modified: 26 Nov 2020 13:51

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