On modelling extreme values

© 2016 Dr. Indriati Njoto BisonoQuantifying changes and the associated uncertainties is critical to the study of climate extremes. In this thesis, extreme values are modelled using a Bayesian framework to understand the behaviour of the extremes. Challenges in modelling extreme climate events include extensive spatial coverage, short time periods and data sparsity. I applied two Bayesian hierarchical models for extremes: a latent model and a max-stable process model. For the former, the data at each site were assumed to follow a generalised extreme value distribution, independent to data at other site. For the latter, the data were assumed to be a realisation of max-stable processes, where a pairwise composite likelihood replaced the full likelihood in estimation. I applied the latent model to the spatial lattice data sets of temperature projections from the regional climate model over Tasmania, Australia, where the spatial dependencies are captured in the second stage using a conditional autoregressive model. The model successfully smoothed the shape parameters and outperformed the simple model that assumed that the extreme values in each grid follow an independent generalised extreme value distribution with particular parameters. For point-referenced data, latent models with random effects were modelled by both a univariate and multivariate Gaussian processes. For a more realistic model for capturing the spatial dependence, the max-stable process model was employed. All models make use of geographical covariates to explain the mean structure of the parameter’s processes. Application of the models to the observed maximum temperatures from 16 sites across Tasmania showed that the max-stable process models showed superior performance based on predictive loss criteria and provided more reasonable estimates and predictions. However, results from the max-stable process model suggest over-concentrated posterior distributions and more pronounced bias. To improve estimation, a modification to the pairwise composite likelihood was proposed and evaluated. Instead of including all possible pairs in the pairwise log-likelihood computation, the region was subset into blocks, and only pairs within neighbouring blocks were included in the log-likelihood. The proposed block pairwise likelihood provided better estimates based on simulation results. Different block sizes were also considered and assessed. The choice of the block size is crucial because there is a trade-off between bias and variance. Based on the simulation finding, the best performance of the estimates was achieved by the block size that distances between pairs within the block neighbourhood were less than or about the same value as the distances where the extremal coefficients were less than or equal to 1.5. On general, smaller block size reduced the complexity of the computation