IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v175y2020icp153-163.html
   My bibliography  Save this article

Fitting the Bartlett–Lewis rainfall model using Approximate Bayesian Computation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475419303313
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2019.10.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    2. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    3. Matteo Richiardi, 2003. "The Promises and Perils of Agent-Based Computational Economics," LABORatorio R. Revelli Working Papers Series 29, LABORatorio R. Revelli, Centre for Employment Studies.
    4. Freyberger, Joachim, 2015. "Asymptotic theory for differentiated products demand models with many markets," Journal of Econometrics, Elsevier, vol. 185(1), pages 162-181.
    5. Rania Gihleb & Osnat Lifshitz, 2022. "Dynamic Effects of Educational Assortative Mating on Labor Supply," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 46, pages 302-327, October.
    6. Lapo Filistrucchi & Tobias J. Klein, 2013. "Price Competition in Two-Sided Markets with Heterogeneous Consumers and Network Effects," Working Papers 13-20, NET Institute.
    7. Yannis M. Ioannides & Vassilis A. Hajivassiliou, 2007. "Unemployment and liquidity constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 479-510.
    8. Pradeep Chintagunta & Jean-Pierre Dubé & Vishal Singh, 2003. "Balancing Profitability and Customer Welfare in a Supermarket Chain," Quantitative Marketing and Economics (QME), Springer, vol. 1(1), pages 111-147, March.
    9. Yai, Tetsuo & Iwakura, Seiji & Morichi, Shigeru, 1997. "Multinomial probit with structured covariance for route choice behavior," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 195-207, June.
    10. Albanesi, Stefania & Gihleb, Rania & Zhang, Ning, 2022. "Boomerang College Kids: Unemployment, Job Mismatch and Coresidence," IZA Discussion Papers 15507, Institute of Labor Economics (IZA).
    11. Igal Hendel, 1994. "Estimating Multiple-Discrete Choice Models: An Application to Computeri-zzation Returns," NBER Technical Working Papers 0168, National Bureau of Economic Research, Inc.
    12. Bolduc, Denis & Kaci, Mustapha, 1993. "Estimation des modèles probit polytomiques : un survol des techniques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(3), pages 161-191, septembre.
    13. Richard Blundell & Monica Costa Dias & Costas Meghir & Jonathan Shaw, 2016. "Female Labor Supply, Human Capital, and Welfare Reform," Econometrica, Econometric Society, vol. 84, pages 1705-1753, September.
    14. Jeremy Lise & Costas Meghir & Jean-Marc Robin, 2016. "Matching, Sorting and Wages," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 19, pages 63-87, January.
    15. Anindya Biswas & Biswajit Mandal, 2016. "Estimating Preference Parameters From Stock Returns Using Simulated Method Of Moments," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-13, March.
    16. Hans G. Bloemen & Arie Kapteyn, 2008. "The estimation of utility-consistent labor supply models by means of simulated scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 395-422.
    17. Calvet, Laurent E. & Czellar, Veronika, 2015. "Through the looking glass: Indirect inference via simple equilibria," Journal of Econometrics, Elsevier, vol. 185(2), pages 343-358.
    18. Keane, Michael & Moffitt, Robert, 1998. "A Structural Model of Multiple Welfare Program Participation and Labor Supply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 553-589, August.
    19. Yi Deng, 2003. "A Dynamic Stochastic Analysis of International Patent Application and Renewal Processes," Computing in Economics and Finance 2003 189, Society for Computational Economics.
    20. Pierre-André Chiappori & Monica Costa Dias & Costas Meghir, 2018. "The Marriage Market, Labor Supply, and Education Choice," Journal of Political Economy, University of Chicago Press, vol. 126(S1), pages 26-72.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:175:y:2020:i:c:p:153-163. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.