Probability and Estimation in Statistics

This lecture covers the fundamental concepts of probability, including events, random variables, distributions, and expectation. It also delves into parametric estimation, discussing observations, shrinkage, testing, and different estimation methods like maximum likelihood and Bayesian estimation. The lecture further explores the linear model, generalized linear models, and the importance of unbiased estimators. Additionally, it touches on testing methodologies, p-values, interval estimation, non-parametric estimation, and Bayesian estimation. The session concludes with a detailed examination of the linear model, including least squares equations, residuals, model building principles, and advanced techniques like ridge regression and the lasso.