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Approximate Bayesian computing for spatial extremes

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  • Erhardt, Robert J.
  • Smith, Richard L.

Abstract

Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian approaches. In this paper, we present a Bayesian approach through the use of approximate Bayesian computing. This circumvents the need for a joint likelihood function by instead relying on simulations from the (unavailable) likelihood. This method is compared with an alternative approach based on the composite likelihood. When estimating the spatial dependence of extremes, we demonstrate that approximate Bayesian computing can provide estimates with a lower mean square error than the composite likelihood approach, though at an appreciably higher computational cost. We also illustrate the performance of the method with an application to US temperature data to estimate the risk of crop loss due to an unlikely freeze event.

Suggested Citation

  • Erhardt, Robert J. & Smith, Richard L., 2012. "Approximate Bayesian computing for spatial extremes," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1468-1481.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1468-1481 DOI: 10.1016/j.csda.2011.12.003
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    References listed on IDEAS

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    1. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    2. Bortot, P. & Coles, S.G. & Sisson, S.A., 2007. "Inference for Stereological Extremes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 84-92, March.
    3. Marc G. Genton & Yanyuan Ma & Huiyan Sang, 2011. "On the likelihood function of Gaussian max-stable processes," Biometrika, Biometrika Trust, vol. 98(2), pages 481-488.
    4. Padoan, S. A. & Ribatet, M. & Sisson, S. A., 2010. "Likelihood-Based Inference for Max-Stable Processes," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 263-277.
    5. 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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    Cited by:

    1. Wang, Yixin & So, Mike K.P., 2016. "A Bayesian hierarchical model for spatial extremes with multiple durations," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 39-56.
    2. McKinley, Trevelyan J. & Ross, Joshua V. & Deardon, Rob & Cook, Alex R., 2014. "Simulation-based Bayesian inference for epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 434-447.

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