Advanced Data Analysis from an Elementary Point of View
by Cosma Rohilla Shalizi
This is a draft textbook on data analysis methods, intended for a one-semester course for advance undergraduate students who have already taken classes in probability, mathematical statistics, and linear regression. It began as the lecture notes for 36-402 at Carnegie Mellon University.
By making this draft generally available, I am not promising to provide any assistance or even clarification whatsoever. Comments are, however, welcome.
The book is under contract to Cambridge University Press; it should be turned over to the press at the end of 2013 or beginning of 2014 in early before the end of 2015. A copy of the next-to-final version will remain freely accessible here permanently.
Complete draft in PDF
Table of contents:
I. Regression and Its Generalizations
The Truth about Linear Regression
Smoothing in Regression
Weighting and Variance
Testing Regression Specifications
Generalized Linear Models and Generalized Additive Models
Classification and Regression Trees
II. Distributions and Latent Structure
Relative Distributions and Smooth Tests of Goodness-of-Fit
Principal Components Analysis
Nonlinear Dimensionality Reduction
III. Dependent Data
Spatial and Network Data
IV. Causal Inference
Graphical Causal Models
Identifying Causal Effects
Causal Inference from Experiments
Estimating Causal Effects
Discovering Causal Structure
Data-Analysis Problem Sets
Reminders from Linear Algebra
Big O and Little o Notation
Algebra with Expectations and Variances
Propagation of Error, and Standard Errors for Derived Quantities
chi-squared and the Likelihood Ratio Test
Proof of the Gauss-Markov Theorem
Rudimentary Graph Theory
Writing R Functions
Random Variable Generation
Unified treatment of information-theoretic topics (relative entropy / Kullback-Leibler divergence, entropy, mutual information and independence, hypothesis-testing interpretations) in an appendix, with references from chapters on density estimation, on EM, and on independence testing
More detailed treatment of calibration and calibration-checking (part II)
Missing data and imputation (part II)
Move d-separation material from “causal models” chapter to graphical models chapter as no specifically causal content (parts II and IV)?
Expand treatment of partial identification for causal inference, including partial identification of effects by looking at all data-compatible DAGs (part IV)
Figure out how to cut at least 50 pages
Make sure notation is consistent throughout: insist that vectors are always matrices, or use more geometric notation?
Move simulation to an appendix
Move variance/weights chapter to right before logistic regression
Move some appendices online (i.e., after references)?
(Text last updated 30 March 2016; this page last updated 6 November 2015)