Lecture Notes on Introductory Statistical Inference

The following are lecture notes I developed over the course of teaching a bridge course on Statistical Inference for incoming graduate students of a Professional Masters in Data Science program at the University of the Philippines. By nature of the program, the students in the course are largely unexposed, or scarcely exposed, to probability theory and statistical inference in general. The goal of the course is to arm the students with some preliminary knowledge of fundamental results often explored in-depth over several undergraduate statistics courses, which they will be requiring in later, more specialized seminars on statistical modeling and machine learning. As a result, these notes attempt to strike a balance tradeoff between intelligibility and comprehensiveness.

Contents

1. Basic Concepts
2. Frequentist Foundations
3. Bayesian Foundations
4. Hypothesis Testing and Estimation
5. Linear Regression and Correlation