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 |
|---|---|---|---|---|
| References can be found in the links or the syllabus | ||||
| 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 | |
| Frequentist inference | Efron & Hastie Chap. 2 | |||
| 5 | Bayesian inference | Efron & Hastie Chap. 3 | ||
| 6-7 | Bootstrap | Efron & Hastie Secs. 10.3, 10.4, 11.1, 11.2 | Shao & Tu (1995) is a neat introduction to the theory of the jackknife and bootstrap. | |
| 9-13 | Causal inference | Ding (2024) A First Course in Causal Inference | Homework 2 due on 5/11. Final report due on June 03. example topics | Simpson’s paradox, potential outcomes, randomization, observational study, stratification, regression adjustment, propensity score, inverse probability weighting, doubly robust estimation, observational study, sensitivity analysis, instrumental variable, proximal causal inference, causal attribution |
| 14-15 | Missing data analysis | Kim and Shao (2021) Statistical Methods for Handling Incomplete Data | Missingness mechanism, MNAR, Heckman’s selection model, nonresponse instrument, shadow variabe, no-self censoring, self censoring, callback |