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Bayesian Inference for Stochastic Cusp Catastrophe Model with Partially Observed Data

Author

Listed:
  • Ding-Geng Chen

    (College of Health Solutions, Arizona State University, Phoenix, AZ 85004, USA
    Department of Statistics, University of Pretoria, Pretoria 0002, South Africa)

  • Haipeng Gao

    (Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USA
    PayPal, Inc., San Jose, CA 95131, USA)

  • Chuanshu Ji

    (Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USA)

Abstract

The purpose of this paper is to develop a data augmentation technique for statistical inference concerning stochastic cusp catastrophe model subject to missing data and partially observed observations. We propose a Bayesian inference solution that naturally treats missing observations as parameters and we validate this novel approach by conducting a series of Monte Carlo simulation studies assuming the cusp catastrophe model as the underlying model. We demonstrate that this Bayesian data augmentation technique can recover and estimate the underlying parameters from the stochastic cusp catastrophe model.

Suggested Citation

  • Ding-Geng Chen & Haipeng Gao & Chuanshu Ji, 2021. "Bayesian Inference for Stochastic Cusp Catastrophe Model with Partially Observed Data," Mathematics, MDPI, vol. 9(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3245-:d:702823
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    References listed on IDEAS

    as
    1. Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
    2. Sims,Christopher A. (ed.), 1996. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521566094.
    3. Grasman, Raoul & van der Maas, Han L.J. & Wagenmakers, Eric-Jan, 2009. "Fitting the Cusp Catastrophe in R: A cusp Package Primer," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i08).
    4. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Ding-Geng Chen & Haipeng Gao & Chuanshu Ji & Xinguang Chen, 2021. "Stochastic cusp catastrophe model and its Bayesian computations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(13-15), pages 2714-2733, November.
    6. Sims,Christopher A. (ed.), 1996. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521566100.
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