Bayesian Flood Frequency Analysis Using Monthly Maxima - Ólafur Birgir Davíðsson 1990- (2014)
In this thesis a statistical flood frequency analysis model is proposed working fully within the framework of Bayesian hierarchical models and latent Gaussian models. The model uses monthly maxima as opposed to the almost exclusive use of annual maxima in field in an attempt to make better use of data in a field where reliable data is hard to come by. At the latent level a generalized linear mixed model is incorporated that accounts for seasonal dependence of parameters and provides a mechanism that allows the model to be extrapolated to river catchments where little or no data is available. The observed data comes from twelve river catchments around Iceland. The choice of data distribution is based on the Gumbel distribution, a special case of the Generalized Extreme Value distribution, and is a complex, high dimensional model that comes with high computational costs. The Markov chain Monte Carlo (MCMC) inference methods make use of a newly developed sampling scheme called the split-sampler pioneered by Óli Páll Geirsson at the University of Iceland to make the sampling process efficient. The specification of prior distributions makes use of Penalizing Complexity Priors to introduce a robust method to infer the latent parameters. The results indicate that the use of monthly maxima are a viable option in flood frequency analysis and that the latent linear mixed model for the likelihood parameters serves as a solid foundation for future research. Í þessari ritgerð er sett fram tölfræðilegt líkan á sviði flóðagreiningar sem fellur undir Bayesísk stigskipt líkön. Líkanið byggist á mælingum um mánaðarleg hágildi á meðan notkun á árlegum hágildum hefur verið venjan í greininni. Með því að notast við mánaðarleg hágildi er reynt að nýta betur þau gögn sem eru til staðar í þar sem áreiðanleg rennslisgögn eru ekki á hverju strái. Undirliggjandi ferli líkansins samanstendur af alhæfðu línulegu líkani með slembiþáttum sem gerir ráð fyrir mánaðarlegri fylgni milli sennileikastika og gefur af sér verkfæri til þess að fá ...