Statistics for Data Science: Introduction to Statistical Methods

This lecture introduces the fundamental concepts of statistics as they apply to data science. The instructor begins by explaining the transition from probability to statistics, emphasizing the importance of understanding data rather than starting with a known distribution. The lecture covers exploratory data analysis, where the instructor highlights the significance of visualizing data to gain insights into its structure and generation process. Following this, the instructor discusses the modeling phase, where hypotheses about data generation are formulated. The lecture also addresses the role of estimators, particularly focusing on the empirical mean and variance, and introduces the method of moments for estimating parameters. The instructor explains the concept of consistency in estimators and the importance of minimizing bias and variance to achieve accurate estimates. Finally, the lecture touches on maximum likelihood estimation, illustrating how to derive estimators for specific distributions, such as the Bernoulli distribution, and discusses the optimality of these estimators in statistical analysis.