This course provides a compact and accessible introduction to statistics, focusing on the most important ideas that have shaped the field and have influenced our ways of viewing and understanding the world. Essential concepts including data, models, algorithms, sampling, likelihood, information, hypothesis testing, regression, and causality will be motivated and introduced. A comparative overview of frequentist and Bayesian inference will be presented. The discussion will be illustrated by examples from the physical, biological, and social sciences.
| Week | Topics | References | Homework | Notes |
|---|---|---|---|---|
| 1 | Introduction | Poldrack Chap. 1 | ||
| 2 | Data, aggregation and visualization | Poldrack Chaps. 2–4 | ColorBrewer 2.0 provides guidance in choosing good colors for your plots. | |
| Benford’s law | Hill (1995), Leemis et al. (2000), Tsagbey et al. (2017) | A more thorough survey of Benford’s law is Berger & Hill (2011). | ||
| 3 | Models, formal theory | Poldrack Chap. 5, McCullagh (2002) | ||
| 4 | Bias–variance trade-off, statistical modeling | ESL Secs. 7.2, 7.3, Breiman (2001) | Homework 1 due on 4/15 | The AIC–BIC dilemma (Yang, 2005) exemplifies the conflict between prediction and inference. Reflections and updates on Breiman’s two cultures in the big data era were given by Donoho (2017) and Efron (2020). |
| Frequentist inference | Efron & Hastie Chap. 2 |