Droughts, exacerbated by anthropogenic climate change, threaten plants through hydraulic failure. This hydraulic failure is caused by the formation of embolisms which block water flow in a plant's xylem conduits. By tracking these failures over time, vulnerability curves (VCs) can be created. The creation of these curves is laborious and time consuming. This study seeks to automate the creation of these curves. In particular, it seeks to automate the optical vulnerability (OV) method of determining hydraulic failure. To do this, embolisms need to be segmented across a sequence of images. Three fully convolutional models were considered for this task, namely U-Net, U-Net (ResNet34), and W-Net. The sample consisted of four unique leaves, each with its own sequence of images. Using these leaves, three experiments were conducted. They considered whether a leaf could generalise across samples from the same leaf, across different leaves of the same species, and across different species. The results were assessed on two levels; the first considered the results of the segmentation, and the second considered how well VCs could be constructed. Across the three experiments, the highest test precision-recall AUCs achieved were 81%, 45%, and 40%. W-Net performed the worst across the models, while U-Net and U-Net (ResNet-34) performed similarly to one another. VC reconstruction was assessed using two metrics. The first is Normalised Root Mean Square Error. The second is the difference in Ψ50 values between the true VC and the predicted VC, where Ψ50 is a physiological value of interest. This study found that the shape of the VCs could be reconstructed well if the model was able to recall a portion of embolisms across all images which had embolisms. Moreover, it found that some images may be more important than others due to a non-linear mapping between time and water potential. VC reconstruction was satisfactory, except for the third experiment. This study demonstrates that, in certain scenarios, automation of the OV method is attainable. To support the ubiquitous use and development of the work done in this study, a website was created to document the code base. In addition, this website contains instructions on how to interact with the code base. For more information please visit: https://plant-network-segmentation.readthedocs.io/.

Policy makers and the government rely heavily on survey data when making policyrelated decisions. Survey data is labour intensive, costly and time consuming, hence it cannot be frequently or extensively collected. The main aim of this research is to demonstrate how Convolutional Neural Network (CNN) coupled with statistical regression modelling can be used to estimate poverty from aerial images supplemented with national household survey data. This provides a more frequent and automated method for updating data that can be used for policy making. This aerial poverty estimation approach is executed in two phases; aerial classification and detection phase and poverty modelling phase. The aerial classification and detection phase use CNN to perform settlement typology classification of the aerial images into three broad geotype classes namely; urban, rural and farm. This is then followed by object detection to detect three broad dwelling type classes in the aerial images namely; brick house, traditional house, and informal settlement. Mask Region-based Convolutional Neural Network (Mask R-CNN) model with a resnet101 CNN backbone model is used to perform this task. The second phase, poverty modelling phase, involves using NIDS data to compute the poverty measure Sen-Shorrocks-Thon (SST) index. This is followed by using regression models to model the poverty measure using aggregated results from the aerial classification and detection phase. The study area for this research is Kwa-Zulu Natal (KZN), South Africa. However, this approach can be extended to other provinces in South Africa, by retraining the models on data associated with the location in question.

The presence of non-linear shape variation in 3D data is known to influence the reliability of linear statistical shape models (SSM). This problem is regularly acknowledged, but disregarded, as it is assumed that linear models are able to adequately approximate such non-linearities. Model reliability is crucial for medical imaging and computer vision tasks; however, prior to modelling, the non-linearity in the data is not often considered. The study provides a framework to identify the presence of non-linearity in using principal component analysis (PCA) and autoencoders (AE) shape modelling methods. The data identified to have linear and non-linear shape variations is used to compare two sophisticated techniques: linear Gaussian process morphable models (GPMM) and non-linear variational autoencoders (VAE). Their model performance is measured using generalisation, specificity and computational efficiency in training. The research showed that, given limited computational power, GPMMs managed to achieve improved relative generalisation performance compared to VAEs, in the presence of non-linear shape variation by at least a factor of six. However, the non-linear VAEs, despite the simplistic training scheme, presented improved specificity generative performance of at least 18% for both datasets.

A variety of species distribution models (SDMs) were fit to data collected by a 15,000km road-side visual survey of Aloidendron dichotomum populations in the Northern Cape region of South Africa, and Namibia. We fit traditional presence/absence SDMs as well as SDMs on how proportions are distributed across three species stage classes (juvenile, adult, dead). Using five candidate machine learning methods and an ensemble model, we compared a number of approaches, including the role of balanced class (presence/absence) datasets in species distribution modelling. Secondary to this was whether or not the addition of species’ absences, generated where the species is known not to exist have an impact on findings. The goal of the analysis was to map the distribution of Aloidendron dichotomum under different scenarios. Precipitation-based variables were generally more deterministic of species presence or lack thereof. Visual interpretation of the estimated Aloidendron dichotomum population under current climate conditions, suggested a reasonably well fit model, having a large overlap with the sampled area. There however were some conditions estimated to be suitable for species incidence outside of the sampled range, where Aloidendron dichotomum are not known to occur. Habitat suitability for juvenile individuals was largely decreasing in concentration towards Windhoek. The largest proportion of dead individuals was estimated to be on the northern edge of the Riemvasmaak Conservancy, along the South African/Namibian boarder, reaching up to a 60% composition of the population. The adult stage class maintained overall proportional dominance. Under future climate scenarios, despite maintaining a bulk of the currently habitable conditions, a noticeable negative shift in habitat suitability for the species was observed. A temporal analysis of Aloidendron dichotomum’s latitudinal and longitudinal range revealed a potential south-easterly shift in suitable species conditions. Results were however met with some uncertainty as SDMs were uncovered to be extrapolating into a substantial amount of the study area. We found that balancing response class frequencies within the data proved not to be an effective error reduction technique overall, having no considerable impact on species detection accuracy. Balancing the classes however did improve the accuracy on the presence class, at the cost of accuracy of the observed absence class. Furthermore, overall model accuracy increased as more absences from outside the study area were added, only because these generated absences were predicted well. The resulting models had lower estimated suitability outside of the survey area and noticeably different suitability distributions within the survey area. This made the addition of the generated absences undesirable. Results highlighted the potential vulnerability of Aloidendron dichotomum given the pessimistic, yet likely future climate scenarios.

The thesis considers the general area of robust portfolio construction. In particular the thesis considers two techniques in this area that aim to improve portfolio construction, and consequently portfolio performance. The first technique focusses on estimation error in the sample covariance (one of portfolio optimisation inputs). In particular shrinkage techniques applied to the sample covariance matrix are considered and the merits thereof are assessed. The second technique considered in the thesis focusses on the portfolio construction/optimisation process itself. Here the thesis adopted the 'resampled efficiency' proposal of Michaud (1989) which utilises Monte Carlo simulation from the sampled distribution to generate a range of resampled efficient frontiers. Thereafter the thesis assesses the merits of combining these two techniques in the portfolio construction process. Portfolios are constructed using a quadratic programming algorithm requiring two inputs: (i) expected returns; and (ii) cross-sectional behaviour and individual risk (the covariance matrix). The output is a set of 'optimal' investment weights, one per each share who's returns were fed into the algorithm. This thesis looks at identifying and removing avoidable risk through a statistical robustification of the algorithms and attempting to improve upon the 'optimal' weights provided by the algorithms. The assessment of performance is done by comparing the out-of-period results with standard optimisation results, which highly sensitive and prone to sampling-error and extreme weightings. The methodology looks at applying various shrinkage techniques onto the historical covariance matrix; and then taking a resampling portfolio optimisation approach using the shrunken matrix. We use Monte-Carlo simulation techniques to replicate sets of statistically equivalent portfolios, find optimal weightings for each; and then through aggregation of these reduce the sensitivity to the historical time-series anomalies. We also consider the trade-off between sampling-error and specification-error of models.

Discrete phylogeographic models enable the inference of the geographic history of biological organisms along phylogenetic trees. Frequently applied in the context of epidemiological modelling, phylogeographic generalised linear models were developed to allow for the evaluation of multiple predictors of spatial diffusion. The standard phylogeographic generalised linear model formulation, however, assumes that rates of spatial diffusion are a noiseless deterministic function of the set of covariates, admitting no other unobserved sources of variation. Under a variety of simulation scenarios, we demonstrate that the lack of a term modelling stochastic noise results in high false positive rates for predictors of spatial diffusion. We further show that the false positive rate can be controlled by including a random effect term, thus allowing unobserved sources of rate variation. Finally, we apply this random effects model to three recently published datasets and contrast the results of analysing these datasets with those obtained using the standard model. Our study demonstrates the prevalence of false positive results for predictors under the standard phylogeographic model in multiple simulation scenarios and, using empirical data from the literature, highlights the importance of a model accounting for random variation.

Commercial sugarcane farming requires large quantities of water to be delivered to the fields. Ideal irrigation schedules are produced indicating how much water to be supplied to fields considering multiple objectives in the farming process. Software packages do not fully account for the fact that the ideal irrigation schedule may not be met due to limitations in the water distribution network. This dissertation proposes the use of mathematical modelling to better understand water supply and demand management on a commercial sugarcane farm. Due to the complex nature of water stress on sugarcane, non-linearities occur in the model. A piecewise linear approximation is used to handle the non-linearity in the water allocation model and is solved in a commercial optimisation software package. A test data set is first used to exercise and evaluate the model performance, then to illustrate the practical applicability of the model, a commercial sized data set is used and analysed.

The e-retail sector in South Africa has a significant opportunity to capture a large portion of the country's retail industry. Central to seizing this opportunity is leveraging the advantages that the online setting affords. In particular, the e-retailer can offer an extremely large catalogue of products; far beyond what a traditional retailer is capable of supporting. However, as the catalogue grows, it becomes increasingly difficult for a customer to efficiently discover desirable products. As a consequence, it is important for the e-retailer to develop tools that automatically explore the catalogue for the customer. In this dissertation, we develop a recommender system (RS), whose purpose is to provide suggestions for products that are most likely of interest to a particular customer. There are two primary contributions of this dissertation. First, we describe a set of six characteristics that all effective RS's should possess, namely; accuracy, responsiveness, durability, scalability, model management, and extensibility. Second, we develop an RS that is capable of serving recommendations in an actual e-retail environment. The design of the RS is an attempt to embody the characteristics mentioned above. In addition, to show how the RS supports model selection, we present a proof-of-concept experiment comparing two popular methods for generating recommendations that we implement for this dissertation, namely, implicit matrix factorisation (IMF) and Bayesian personalised ranking (BPR).

Since the establishment of Markowitz's theory, numerous studies have been carried out over the past six decades or so that cover the benefits, limitations, modifications and enhancements of Mean Variance (MV) optimisation. This study endeavours to extend on this, by means of adding factors to the minimum variance framework, which would increase the likelihood of outperforming both the market and the minimum variance portfolio (MVP). An analysis of the impact of these factor tilts on the MVP is carried out in the South African environment, represented by the FTSE-JSE Shareholder weighted Index as the benchmark portfolio. The main objective is to examine if the systematic and robust methods employed, which involve the incorporation of factor tilts into the multicriteria problem, together with covariance shrinkage – improve the performance of the MVP. The factor tilts examined include Active Distance, Concentration and Volume. Additionally, the constant correlation model is employed in the estimation of the shrinkage intensity, structured covariance target and shrinkage estimator. The results of this study showed that with specific levels of factor tilting, one can generally improve both absolute and risk-adjusted performance and lower concentration levels in comparison to both the MVP and benchmark. Additionally, lower turnover levels were observed across all tilted portfolios, relative to the MVP. Furthermore, covariance shrinkage enhanced all portfolio statistics examined, but significant improvement was noted on drawdown levels, capture ratios and risk. This is in contrast to the results obtained when the standard sample covariance matrix was employed.

Business Intelligence (BI) techniques provide the potential to not only efficiently manage but further analyse and apply the collected information in an effective manner. Benefiting from research both within industry and academia, BI provides functionality for accessing, cleansing, transforming, analysing and reporting organisational datasets. This provides further opportunities for the data to be explored and assist organisations in the discovery of correlations, trends and patterns that exist hidden within the data. This hidden information can be employed to provide an insight into opportunities to make an organisation more competitive by allowing manager to make more informed decisions and as a result, corporate resources optimally utilised. This potential insight provides organisations with an unrivalled opportunity to remain abreast of market trends. Consequently, BI techniques provide significant opportunity for integration with Decision Support Systems (DSS). The gap which was identified within the current body of knowledge and motivated this research, revealed that currently no suitable framework for BI, which can be applied at a meta-level and is therefore tool, technology and domain independent, currently exists. To address the identified gap this study proposes a meta-level framework: - ‘KDDS-BI’, which can be applied at an abstract level and therefore structure a BI investigation, irrespective of the end user. KDDS-BI not only facilitates the selection of suitable techniques for BI investigations, reducing the reliance upon ad-hoc investigative approaches which rely upon ‘trial and error’, yet further integrates Knowledge Management (KM) principles to ensure the retention and transfer of knowledge due to a structured approach to provide DSS that are based upon the principles of BI. In order to evaluate and validate the framework, KDDS-BI has been investigated through three distinct case studies. First KDDS-BI facilitates the integration of BI within ‘Direct Marketing’ to provide innovative solutions for analysis based upon the most suitable BI technique. Secondly, KDDS-BI is investigated within sales promotion, to facilitate the selection of tools and techniques for more focused in store marketing campaigns and increase revenue through the discovery of hidden data, and finally, operations management is analysed within a highly dynamic and unstructured environment of the London Underground Ltd. network through unique a BI solution to organise and manage resources, thereby increasing the efficiency of business processes. The three case studies provide insight into not only how KDDS-BI provides structure to the integration of BI within business process, but additionally the opportunity to analyse the performance of KDDS-BI within three independent environments for distinct purposes provided structure through KDDS-BI thereby validating and corroborating the proposed framework and adding value to business processes.