Dr. Tshilidzi Marwala is the Rector of the United Nations (UN) University and the UN Under-Secretary-General from 1 March 2023. He was previously the Vice-Chancellor and Principal of the University of Johannesburg, Deputy Vice-Chancellor for Research and Executive Dean of the Faculty of Engineering at the University of Johannesburg. He was Associate Professor, Full Professor, the Carl and Emily Fuchs Chair of Systems and Control Engineering at the University of the Witwatersrand. He holds a Bachelor of Science in Mechanical Engineering (magna cum laude) from Case Western Reserve University, a Master of Mechanical Engineering from the University of Pretoria, PhD in Artificial Intelligence from the University of Cambridge and a Post-Doc at Imperial College (London). He is a registered professional engineer, a Fellow of TWAS (The World Academy of Sciences), the Academy of Science of South Africa, the African Academy of Sciences and the South African Academy of Engineering. He is a Senior Member of the IEEE and a distinguished member of the ACM. His research interests are multi-disciplinary and they include the theory and application of artificial intelligence toengineering, computer science, finance, social science and medicine. He has supervised 28 Doctoral students published 15 books in artificial intelligence (one translated into Chinese), over 300 papers in journals, proceedings, book chapters and magazines and holds five patents. He is an associate editor of the International Journal of Systems Science (Taylor and Francis Publishers). He has been a visiting scholar at Harvard University, University of California at Berkeley, Wolfson College of the University of Cambridge, Nanjing Tech University and Silesian University of Technology in Poland. His opinions have appeared in the New Scientist, The Economist, Time Magazine, BBC, CNN and the Oxford Union. Dr. Marwala is the author of Rational Machines and Artificial Intelligence from Elsevier Academic Press. Dr. Rendani Mbuvha is a lecturer in Statistics and Actuarial Science at the University of Witwatersrand, Johannesburg, South Africa. He is a qualified Actuary and a holder of the Chartered Enterprise Risk Actuary designation. He holds a BSc with Honors in Actuarial Science and Statistics from the University of Cape Town, an MSc in Machine Learning from KTH, Royal Institute of Technology in Sweden, and a Ph.D. in Probabilistic Parameter Inference at the University of Johannesburg. He was a recipient of the Google Ph.D. fellowship for his research at the University of Johannesburg. He has previously served in various analytics and actuarial roles in large financial services and AI consulting organizations in both South Africa and Sweden. Dr Wilson Tsakane Mongwe holds a PhD in Artificial Intelligence from the University of Johannesburg and was selected as a Google PhD Fellow in Machine Learning, one of only sixteen recipients worldwide. He serves as a Visiting Lecturer at the University of the Witwatersrand, where he co-supervises postgraduate research and contributes to teaching in machine learning and computational methods. His academic work centers on scalable Bayesian inference, including Hamiltonian Monte Carlo, Laplace approximation, and variational techniques, with applications spanning computational finance, risk modelling, and sustainable development. He has authored two academic books, Hamiltonian Monte Carlo Methods in Machine Learning (Elsevier, 2023) and Bayesian Machine Learning in Quantitative Finance (Springer, 2025), alongside more than twenty peer-reviewed publications appearing in venues such as IEEE Access, PLoS ONE, and NeurIPS workshops. His research bridges probabilistic machine learning theory with real-world decision-making challenges across financial, environmental, and governance domains.

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• 1. Introduction to Hamiltonian Monte Carlo2. Sampling Benchmarks and Performance Metrics3. Stochastic Volatility Metropolis-Hastings4. Quantum-Inspired Magnetic Hamiltonian Monte Carlo5. Generalised Magnetic and Shadow Hamiltonian Monte Carlo6. Shadow Hamiltonian Monte Carlo Methods7. Adaptive Shadow Hamiltonian Monte Carlo Methods8. Adaptive Noncanonical Hamiltonian Monte Carlo9. Antithetic Hamiltonian Monte Carlo Techniques10. Application: Bayesian Neural Network Inference in Wind Speed Forecasting11. Application: A Bayesian Analysis of Lockdown Alert Level Framework for Combating COVID-1912. Application: Probabilistic Inference of Equity Option Prices Under Jump-Di13. Application: Bayesian Inference of Local Government Audit Outcomes14. Open Problems in SamplingAppendixA: Separable Shadow HamiltonianB: Automatic Relevance DeterminationC: Audit Outcome Literature Survey