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Fitting the Bartlett–Lewis rainfall model using Approximate Bayesian Computation

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  • Aryal, Nanda R.
  • Jones, Owen D.

Abstract

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 t 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.

Suggested Citation

  • Aryal, Nanda R. & Jones, Owen D., 2020. "Fitting the Bartlett–Lewis rainfall model using Approximate Bayesian Computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 175(C), pages 153-163.
    • Handle: RePEc:eee:matcom:v:175:y:2020:i:c:p:153-163
    DOI: 10.1016/j.matcom.2019.10.018
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    References listed on IDEAS

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    1. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    3. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
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    1. Nadarajah I Ramesh & Gayatri Rode & Christian Onof, 2022. "A Cox Process with State-Dependent Exponential Pulses to Model Rainfall," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(1), pages 297-313, January.

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