Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.
Introduces Scientific Machine Learning, emphasizing its application in various scientific fields and the connection between machine learning and physics.
Covers the basics of linear regression, OLS method, predicted values, residuals, matrix notation, goodness-of-fit, hypothesis testing, and confidence intervals.
Covers Markov Chain Monte Carlo for sampling high-dimensional distributions, discussing challenges, advantages, and applications like the Knapsack Problem and cryptography.
Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.