Statistical Inference

What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly reporting p-values and claiming statistical significance for scientifically insignificant results. In these notes statistics is viewed as a branch of mathematical engineering, that studies ways of extracting reliable information from limited data for learning, prediction, and decision making in the presence of uncertainty. The main goals of these notes are: (1) provide a logical introduction to statistical inference, (2) develop statistical thinking and intuitive feel for the subject, and (3) introduce the most fundamental ideas, concepts, and methods of statistics, explain how and why they work, and when they don't. These lecture notes are based on the courses the author taught at the University of Southern California in 2012 and 2013, and at the California Institute of Technology in 2016 and 2017