Estimation of Extremes: Conventional versus Bayesian techniques

The Bayesian and Maximum Likelihood (ML) estimators of surges at two stations of the Dutch coast on the North Sea are compared herein. The ML approach is commonly used, while the Bayesian approach allows both for a parameter uncertainty and a randomness inclusion in future observations. In the Bayesian framework, two different ways of constructing prior distributions are examined, namely the near flat distributions for model parameters and the incorporation of information from neighborhood sites of that under consideration through the distribution of quantile differences. The Bayesian framework offers substantial advantages to analyze the extreme values in both cases. The analysis is also performed using log-transformed surge data. This selection is proven to be advantageous for naturally bounded variables and to better capture the “relative” character of extremes.