Iterative Stochastic Numerical Methods for Statistical Sampling

This course aims to teach learners about the design, analysis, and implementation of algorithms for time-dependent phenomena and modeling in engineering and the sciences. The course focuses on providing efficient deterministic and stochastic numerical methods for various applications, including molecular simulation and Bayesian inference from data. Students will learn about stochastic algorithms for statistical sampling, with a particular emphasis on the crossover of techniques from molecular science to data analytics. The course covers the interplay between data science approaches and models based on physical laws and mathematical structures, aiming to merge Bayesian inference with traditional models grounded in physical principles. The teaching method of the course involves a research-based approach, exploring the connections between data science, statistics, operational research, and machine learning. The course is designed for learners interested in numerical methods, statistical sampling, data analytics, and the application of mathematical models in engineering and the sciences.