In designing ocean structures, estimating the largest wave height it may encounter over its lifetime is a critical issue, but wave observation data is often sparse in space and time. Because of the limited data available, estimation errors are inevitably large. For an economical and robust structure design, the probability density function of the extreme wave height and its confidence interval must be theoretically quantified from limited information available.
Extreme values estimations have been made by finding the best fitting distribution from limited observations, and extrapolating it for the desired long period. Estimations based on frequentist method lack of generality in confidence interval estimations, especially when the data size is small. Another technique recently developed is based on Bayesian Statistics, which provides the inference of uncertainty. Previous studies use informative and non-informative priors and Markov Chain Monte Carlo (MCMC) simulation for estimation.
We have developed a “Likelihood-Weighted Method (LWM)” to objectively evaluate probability density function of the extreme value. The method is based on Extreme Theory and Bayesian Statistics. Our attempt is to use the ignorant prior to relate each parameter set’s likelihood to its probability. This method is pragmatic, because the numerical implementation does not require the use of MCMC.
The theoretical background and practical advantages of LWM are described. Examples from randomly produced data show the performance of this method, and application to real wave data reveals the poor estimations of previous methods that do not use the Bayesian theorem. The quantification of probability for each extreme value distribution enables the probability-weighted evaluation for inference such as maximum wave height probability density function. The new inference derived from this method is useful to change structure design methodologies of ocean structures.