Fjalarr Páll Mánason heldur fyrirlestur um verkefni sitt til meistaraprófs í fjármálaverkfræði við Iðnaðarverkfræði-, vélaverkfræði- og tölvunarfræðideild.
Abstract:
The purpose of this project is to build a model which can conduct flood analysis on any river, given the proper data. This is done using extreme value theory with Bayesian statistics and Markov chain Monte Carlo (MCMC) simulations for posterior inference. Two types of extreme value models are constructed, namely, a block maxima model and a threshold model. The block maxima model uses annual maximum values of discharge for flood analysis while a threshold model uses discharge values exceeding a certain threshold. Methods for choosing an appropriate threshold value for the threshold model are investigated.The data used in the block maxima model are fitted to the generalized extreme value (GEV) distribution and the data used in the threshold model are fitted to the generalized Pareto (GP) distribution. The three parameter GEV distribution and the two parameter GP distribution both have a shape parameter which controls the shape of the tails of the distributions. A negative shape parameter leads to a bounded upper tail leading to an upper limit on extremes. For a non-negative shape parameter the tails of the distributions become unbounded and the tails grow thicker as the value of the shape parameter increases leading to a higher probability of large values. Using the Bayesian methodology it is explored whether constraining the shape parameter, using prior knowledge, is beneficiary and if it is statistically acceptable.
The goal is to understand the behavior of a river and predict the magnitude of water discharge likely to arise over a particular time span. This magnitude of discharge is visually described in return level plots. The uncertainty in the return level plots is often quite large. The uncertainty in an extreme value analysis is of major importance. One source of uncertainty is due to sampling. There is another source of uncertainty taken into account in the thesis. Namely, the uncertainties in the discharge values. The discharge is found by transformation from water level using a discharge rating curve. Whether the discharge rating curve uncertainty has a significant effect on the over all uncertainty in return level plots or not, is studied.
The parameters of the GEV and GP distributions are evaluated through the Bayesian approach. Posterior densities are compared for the two different types of models (GEV and GP) using three different cases of prior distributions with and without a discharge rating curve uncertainty. This comparison is done for four rivers in Iceland.
Umsjónakennari: Ólafur Pétur Pálsson
Leiðbeinendur Birgir Hrafnkelsson og Sigurður Magnús Garðarsson
Fulltrúi deildar: Daníel F. Guðbjartsson
