The Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has highlighted the need for performing accurate inference with limited data. Fundamental to the design of rapid state responses is the ability to perform epidemiological model parameter inference for localised trajectory predictions. In this work, we perform Bayesian parameter inference using Markov Chain Monte Carlo (MCMC) methods on the Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological models with time-varying spreading rates for South Africa. The results find two change points in the spreading rate of COVID-19 in South Africa as inferred from the confirmed cases. The first change point coincides with state enactment of a travel ban and the resultant containment of imported infections. The second change point coincides with the start of a state-led mass screening and testing programme which has highlighted community-level disease spread that was not well represented in the initial largely traveller based and private laboratory dominated testing data. The results further suggest that due to the likely effect of the national lockdown, community level transmissions are slower than the original imported case driven spread of the disease.

Solar irradiance forecasting is essential in renewable energy grids amongst others for back-up programming, operational planning, and short-term power purchases. This study focuses on forecasting hourly solar irradiance using data obtained from the Southern African Universities Radiometric Network at the University of Pretoria radiometric station. The study compares the predictive performance of long short-term memory (LSTM) networks, support vector regression and feed forward neural networks (FFNN) models for forecasting short-term solar irradiance. While all the models outperform principal component regression model, a benchmark model in this study, the FFNN yields the lowest mean absolute error and root mean square error on the testing set. Empirical results show that the FFNN model produces the most accurate forecasts based on mean absolute error and root mean square error. Forecast combination of machine learning models’ forecasts is done using convex combination and quantile regression averaging (QRA). The predictive performance we found is statistically significant on the Diebold Mariano and Giacomini-White tests. Based on all the forecast accuracy measures used in this study including the statistical tests, QRA is found to be the best forecast combination method. QRA was also the best forecasting model compared with the stand-alone machine learning models. The median method for combining interval limits gives the best results on prediction interval widths analysis. This is the first application of LSTM on South African and African solar irradiance data to the best of our knowledge. This study has shown that providing adequate and detailed evaluation metrics, including statistical tests in forecasting gives more insight into the developed forecasting models.

Wind offers an environmentally sustainable energy resource that has seen increasing global adoption in recent years. However, its intermittent, unstable and stochastic nature hampers its representation among other renewable energy sources. This work addresses the forecasting of wind speed, a primary input needed for wind energy generation, using data obtained from the South African Wind Atlas Project. Forecasting is carried out on a two days ahead time horizon. We investigate the predictive performance of artificial neural networks (ANN) trained with Bayesian regularisation, decision trees based stochastic gradient boosting (SGB) and generalised additive models (GAMs). The results of the comparative analysis suggest that ANN displays superior predictive performance based on root mean square error (RMSE). In contrast, SGB shows outperformance in terms of mean average error (MAE) and the related mean average percentage error (MAPE). A further comparison of two forecast combination methods involving the linear and additive quantile regression averaging show the latter forecast combination method as yielding lower prediction accuracy. The additive quantile regression averaging based prediction intervals also show outperformance in terms of validity, reliability, quality and accuracy. Interval combination methods show the median method as better than its pure average counterpart. Point forecasts combination and interval forecasting methods are found to improve forecast performance.

Hamiltonian Monte Carlo is a Markov Chain Monte Carlo method that has been widely applied to numerous posterior inference problems within the machine learning literature. Markov Chain Monte Carlo estimators have higher variance than classical Monte Carlo estimators due to autocorrelations present between the generated samples. In this work we present three new methods for tackling the high variance problem in Hamiltonian Monte Carlo based estimators: 1) We combine antithetic and importance sampling techniques where the importance sampler is based on sampling from a modified or shadow Hamiltonian using Separable Shadow Hamiltonian Hybrid Monte Carlo, 2) We present the antithetic Magnetic Hamiltonian Monte Carlo algorithm that is based on performing antithetic sampling on the Magnetic Hamiltonian Monte Carlo algorithm and 3) We propose the antithetic Magnetic Momentum Hamiltonian Monte Carlo algorithm based on performing antithetic sampling on the Magnetic Momentum Hamiltonian Monte Carlo method. We find that the antithetic Separable Shadow Hamiltonian Hybrid Monte Carlo and antithetic Magnetic Momentum Hamiltonian Monte Carlo algorithms produce effective sample sizes that are higher than antithetic Hamiltonian Monte Carlo on all the benchmark datasets. We further find that antithetic Separable Shadow Hamiltonian Hybrid Monte Carlo and antithetic Magnetic Hamiltonian Monte Carlo produce higher effective sample sizes normalised by execution time in higher dimensions than antithetic Hamiltonian Monte Carlo. In addition, the antithetic versions of all the algorithms have higher effective sample sizes than their non-antithetic counterparts, indicating the usefulness of adding antithetic sampling to Markov Chain Monte Carlo algorithms. The methods are assessed on benchmark datasets using Bayesian logistic regression and Bayesian neural network models.

Good financial management provides economic stability and sustainability to an organization. It enables an organisation to make good use of its resources and plan effectively. South Africa’s public financial management has deteriorated over time, with only 16% of municipalities receiving a clean audit in the 2020-21 financial period as reported by the Auditor General of South Africa. This work aims to find an appropriate model for analysing and predicting audit outcomes for South African municipalities. The data used in the study include 1560 observations of which 55% were unqualified audit opinions. The features used are 13 financial ratios obtained from financial statements from years 2012 to 2018. Feature selection is performed using random forest, correlation analysis and stepwise regression analysis. The performances of three machine learning algorithms are compared; decision tree, artificial neural network (ANN) and logistic regression models. The findings indicate that ANN is the appropriate model for predicting audit opinions in South African municipalities with overall average area under the receiver operating characteristic curve of 0.6918 and overall average area under the Precision–Recall curve of 0.7074 across all feature selection methods. In addition, debt to operating ratio, current ratio and net operating surplus margin are found to be the common three important financial ratios across the various feature selection techniques.