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, *generally* 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~~ by the end of 2018, inshallah. A copy of the
next-to-final version will remain freely accessible here permanently.

Table of contents:

- Regression Basics
- The Truth about Linear Regression
- Model Evaluation
- Smoothing in Regression
- Simulation
- The Bootstrap
- Splines
- Additive Models
- Testing Regression Specifications
- Weighting and Variance
- Logistic Regression
- Generalized Linear Models and Generalized Additive Models
- Classification and Regression Trees

II. Distributions and Latent Structure - Density Estimation
- Relative Distributions and Smooth Tests of Goodness-of-Fit
- Principal Components Analysis
- Factor Models
- Nonlinear Dimensionality Reduction
- Mixture Models
- Graphical Models

III. Causal Inference - Graphical Causal Models
- Identifying Causal Effects
- Causal Inference from Experiments
- Estimating Causal Effects
- Discovering Causal Structure

IV. Dependent Data - Time Series
- Simulation-Based Inference

Appendices- Data-Analysis Problem Sets
- Reminders from Linear Algebra
- Big O and Little o Notation
- Taylor Expansions
- Multivariate Distributions
- Algebra with Expectations and Variances
- Propagation of Error, and Standard Errors for Derived Quantities
- Optimization
- chi-squared and the Likelihood Ratio Test
- Rudimentary Graph Theory
- Information Theory and Convexity
- Writing R Functions
- Random Variable Generation

I. Regression and Its Generalizations

Planned changes:

- 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 [begun]
- 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 some appendices online (i.e., after references)?

(Text last updated 9 September 2018; this page last updated 10 September 2018)