Logo Gwerddon
Y Coleg Cymraeg Cenedlaethol
Chwilio
Cymraeg / English

Cynrychioliad amharamedrig ar gyfer cyd-newidynnau amlddimensiynol mewn model gwerthoedd eithaf, â chymhwysiad eigionegol

Back
Cynrychioliad amharamedrig ar gyfer cyd-newidynnau amlddimensiynol mewn model gwerthoedd eithaf, â chymhwysiad eigionegol
(A non-parametric representation for multi-dimensional covariates in an extreme value model, with oceanographic application)

Philip Jonathan

A statistical methodology is presented to model extreme values from non-stationary environmental processes. The methodology is based on a generalized Pareto model for peaks over threshold of the environmental process combined with a Voronoi representation for the variation of extreme value model parameters with multi-dimensional covariates. Bayesian inference using reversible-jump MCMC, incorporating Metropolis-Hastings within Gibbs sampling, is used to estimate the joint posterior distribution of all parameters of the Voronoi representation. The methodology is applied to characterise extreme ocean storm severity with direction and season. The fitted model is validated by comparing the characteristics of data simulated under the model with those of the original sample data. Further, the model is used to estimate the distribution of maxima of peaks over threshold corresponding to return periods much longer than the period of the original data.

2,672 Kb

Reference:

 
  	Philip Jonathan, ‘Cynrychioliad amharamedrig ar gyfer cyd-newidynnau amlddimensiynol mewn model gwerthoedd eithaf, â chymhwysiad eigionegol’, Gwerddon, 33, October 2021, 68–84.

Keywords

 
    Extreme value, multi-dimensional covariate, Voronoi partition, Bayesian inference, Gibbs sampling and Metropolis-Hastings, reversible-jump MCMC, ocean wave, return value.

Bibliography:

 
  	
    

  1. Bao, Y., Song, Z., a Qiao, F. (2020), ‘FIO-ESM version 2.0: Model description and evaluation’, Journal of Geophysical Research: Oceans, 125, e2019JC016036.
    2. 

  2. Battjes, J.A., a Groenendijk, H.W. (2000), ‘Wave height distributions on shallow fores- hores’, Coastal Engineering 40, 161–82.
    3. 

  3. Beirlant, J., et al. (2004), Statistics of extremes: theory and applications (Wiley, Chi- chester, UK).
    4. 

  4. Bloemendaal, N., et al. (2020), ‘Generation of a global synthetic tropical cyclone hazard dataset using storm’, Scientific Data, 7, 1–12.
    5. 

  5. Bodin, T., Sambridge, M., a Gallagher, K., (2009), ‘A self-parametrizing partition model approach to tomographic inverse problems’, Inverse Problems, 25, 055009.
    6. 

  6. Coles, S. (2001), An introduction to statistical modelling of extreme values (Springer, London).
    7. 

  7. Coles, S.G., a Powell, E.A. (1996), ‘Bayesian methods in extreme value modelling: a review and new developments’, International Statistics Review, 64, 119–36.
    8. 

  8. Davison, A.C., Padoan, S.A., a Ribatet, M. (2012), ‘Statistical modelling of spatial extremes’, Statistical Science, 27, 161–86.
    9. 

  9. Ewans, K.C., a Jonathan, P. (2008), ‘The effect of directionality on northern North Sea extreme wave design criteria’, Journal of Offshore Mechanics and Arctic Engineering, 130, 041604:1–8.
    10. 

  10. Gamerman, D., a Lopes, H.F. (2006), Markov chain Monte Carlo: stochastic simulation for Bayesian inference (Chapman and Hall / CRC, Boca Raton, USA).
    11. 

  11. Green, P. (1995), ‘Reversible jump Markov chain Monte Carlo computation and Bayesian model determination’, Biometrika, 82, 711–32.
    12. 

  12. Heffernan, J.E., a Tawn, J.A. (2004), ‘A conditional approach for multivariate extreme values’, Journal of the Royal Statistical Society B, 66, 497–546.
    13. 

  13. ISO19901-1 (2015), Petroleum and natural gas industries. Specific requirements for offshore structures. Part 1: Metocean design and operating considerations, argraffiad cyntaf (International Standards Organisation).
    14. 

  14. Jonathan, P., ac Ewans, K.C. (2008), ‘On modelling seasonality of extreme waves’, yn: Proc. 27th International Conf. on Offshore Mechanics and Arctic Engineering, 4-8 June, Estoril, Portugal.
    15. 

  15. Jonathan, P., ac Ewans, K.C. (2011), ‘Modelling the seasonality of extreme waves in the Gulf of Mexico’, Journal of Offshore Mechanical and Arctic Engineering, 133: 021104.
    16. 

  16. Jonathan, P., ac Ewans, K.C., (2013), ‘Statistical modelling of extreme ocean environ- ments with implications for marine design: a review’, Ocean Engineering, 62, 91–109.
    17. 

  17. Jonathan, P., et al. (2021), ‘Uncertainties in return values from extreme value analysis    of peaks over threshold using the generalized Pareto distribution’, Ocean Engineering, 220, 107725.
    18. 

  18. Kinsman, B. (2012), Wind waves: Their generation and propagation on the ocean surface(Dover: New York).
    19. 

  19. NORSOK N-006 (2015), NORSOK Standard N-006:2015: Assessment of structural integrity for existing offshore load-bearing structures (NORSOK, Norway).
    20. 

  20. Northrop, P., Attalides, N., a Jonathan, P. (2017), ‘Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity’, Journal of the Royal Statistical Society C, 66, 93–120.
    21. 

  21. Pickands, J. (1975), ‘Statistical inference using extreme order statistics’, Annals of Statistics, 3, 119–31.
    22. 

  22. Randell, D., et al. (2015), ‘Distributions of return values for ocean wave characteristics in the South China Sea using directional-seasonal extreme value analysis’, Environmetrics, 26, 442–50.
    23. 

  23. Randell, D., et al. (2016), ‘Bayesian inference for non-stationary marginal extremes’, Environmetrics, 27, 439–50.
    24. 

  24. Reistad, M., et al. (2011), ‘A high-resolution hindcast of wind and waves for the North Sea, the Norwegian Sea, and the Barents Sea’, Journal of Geophysical Research, 116, 1–18.
    25. 

  25. Zanini, E., et al. (2020), ‘Covariate representations for non-stationary extremes’, Environmetrics, e2624.
    26.