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Finite mixture modelling is a powerful and well-developed paradigm, having proven useful in unsupervised learning and, to a lesser extent supervised learning (mixture discriminant analysis), especially in the case(s) of data with local variation and/or latent variables. It is the aim of this thesis to improve upon mixture discriminant analysis by introducing two types of random forest analogues which are called Mix- Forests. The first MixForest is based on Gaussian mixture models from the famous family of Gaussian parsimonious clustering models and will be useful in classify- ing lower dimensional data. The second MixForest extends the technique to higher dimensional data via the use of mixtures of factor analyzers from the well-known family of parsimonious Gaussian mixture models. MixForests will be utilized in the analysis of real data to demonstrate potential increases in classification accuracy as well as inferential procedures such as generalization error estimation and variable importance measures. / Thesis / Doctor of Philosophy (PhD)

The number of flood events and the estimated costs of floods have increased dramatically over the past few decades. To reduce the negative impacts of flooding, reliable flood forecasting is essential for early warning and decision making. Although various flood forecasting models and techniques have been developed, the assessment and reduction of uncertainties associated with the forecast remain a challenging task. Therefore, this thesis focuses on the investigation of Bayesian methods for producing probabilistic flood forecasts to accurately quantify predictive uncertainty and enhance the forecast performance and reliability. In the thesis, hydrologic uncertainty was quantified by a Bayesian post-processor - Hydrologic Uncertainty Processor (HUP), and the predictability of HUP with different hydrologic models under different flow conditions were investigated. Followed by an extension of HUP into an ensemble prediction framework, which constitutes the Bayesian Ensemble Uncertainty Processor (BEUP). Then the BEUP with bias-corrected ensemble weather inputs was tested to improve predictive performance. In addition, the effects of input and model type on BEUP were investigated through different combinations of BEUP with deterministic/ensemble weather predictions and lumped/semi-distributed hydrologic models. Results indicate that Bayesian method is robust for probabilistic flood forecasting with uncertainty assessment. HUP is able to improve the deterministic forecast from the hydrologic model and produces more accurate probabilistic forecast. Under high flow condition, a better performing hydrologic model yields better probabilistic forecast after applying HUP. BEUP can significantly improve the accuracy and reliability of short-range flood forecasts, but the improvement becomes less obvious as lead time increases. The best results for short-range forecasts are obtained by applying both bias correction and BEUP. Results also show that bias correcting each ensemble member of weather inputs generates better flood forecast than only bias correcting the ensemble mean. The improvement on BEUP brought by the hydrologic model type is more significant than the input data type. BEUP with semi-distributed model is recommended for short-range flood forecasts. / Dissertation / Doctor of Philosophy (PhD) / Flood is one of the top weather related hazards and causes serious property damage and loss of lives every year worldwide. If the timing and magnitude of the flood event could be accurately predicted in advance, it will allow time to get well prepared, and thus reduce its negative impacts. This research focuses on improving flood forecasts through advanced Bayesian techniques. The main objectives are: (1) enhancing reliability and accuracy of flood forecasting system; and (2) improving the assessment of predictive uncertainty associated with the flood forecasts. The key contributions include: (1) application of Bayesian forecasting methods in a semi-urban watershed to advance the predictive uncertainty quantification; and (2) investigation of the Bayesian forecasting methods with different inputs and models and combining bias correction technique to further improve the forecast performance. It is expected that the findings from this research will benefit flood impact mitigation, watershed management and water resources planning.