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


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

Cyflwynir methodoleg ystadegol er mwyn modelu gwerthoedd eithaf amgylcheddol prosesau anunfan. Seilir y fethodoleg ar fodel Pareto cyffredinoledig ar gyfer brigau dros drothwy o'r broses amgylcheddol, â chynrychioliad Voronoi ar gyfer amrywiad paramedrau'r model gwerthoedd eithaf gyda chyd-newidynnau amlddimensiynol. Defnyddir rhesymu Bayesaidd MCMC naid wrthdroadwy, yn ymgorffori samplu Metropolis-Hastings mewn Gibbs, i amcangyfrif cyd-ol-ddosraniad holl baramedrau'r cynrychioliad Voronoi. Cymhwysir y fethodoleg i ganfod nodweddion gerwinder stormydd morol eithafol gyda chyfeiriad a thymor. Dilysir bod efelychiadau yn ôl y model a amcangyfrifwyd yn cyfateb yn dda i'r data gwreiddiol. Ymhellach, defnyddir y model i amcangyfrif uchafwerthoedd brigau dros drothwy sy'n cyfateb i gyfnodau dychwelyd llawer hwy na chyfnod y data gwreiddiol.


Cyfeiriad:

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

Allweddeiriau

 
    Gwerthoedd eithaf, cyd-newidyn amlddimensiynol, ymraniad Voronoi, rhesymu Bayesaidd, samplu Gibbs a Metropolis-Hastings, samplu MCMC naid wrthdroadwy, tonnau morol, gwerth dychwelyd.
    

Llyfryddiaeth:

 
  	
  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. Battjes, J.A., a Groenendijk, H.W. (2000), ‘Wave height distributions on shallow fores- hores’, Coastal Engineering 40, 161–82.
  3. Beirlant, J., et al. (2004), Statistics of extremes: theory and applications (Wiley, Chi- chester, UK).
  4. Bloemendaal, N., et al. (2020), ‘Generation of a global synthetic tropical cyclone hazard dataset using storm’, Scientific Data, 7, 1–12.
  5. Bodin, T., Sambridge, M., a Gallagher, K., (2009), ‘A self-parametrizing partition model approach to tomographic inverse problems’, Inverse Problems, 25, 055009.
  6. Coles, S. (2001), An introduction to statistical modelling of extreme values (Springer, London).
  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. Davison, A.C., Padoan, S.A., a Ribatet, M. (2012), ‘Statistical modelling of spatial extremes’, Statistical Science, 27, 161–86.
  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. Gamerman, D., a Lopes, H.F. (2006), Markov chain Monte Carlo: stochastic simulation for Bayesian inference (Chapman and Hall / CRC, Boca Raton, USA).
  11. Green, P. (1995), ‘Reversible jump Markov chain Monte Carlo computation and Bayesian model determination’, Biometrika, 82, 711–32.
  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. 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. 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. 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. 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. 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. Kinsman, B. (2012), Wind waves: Their generation and propagation on the ocean surface(Dover: New York).
  19. NORSOK N-006 (2015), NORSOK Standard N-006:2015: Assessment of structural integrity for existing offshore load-bearing structures (NORSOK, Norway).
  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. Pickands, J. (1975), ‘Statistical inference using extreme order statistics’, Annals of Statistics, 3, 119–31.
  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. Randell, D., et al. (2016), ‘Bayesian inference for non-stationary marginal extremes’, Environmetrics, 27, 439–50.
  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. Zanini, E., et al. (2020), ‘Covariate representations for non-stationary extremes’, Environmetrics, e2624.