🔖 Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi

Bookmarked Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi (stat.cmu.edu)

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 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

Regression Basics

The Truth about Linear Regression

Model Evaluation

Smoothing in Regression

Simulation

The Bootstrap

Weighting and Variance

Splines

Additive Models

Testing Regression Specifications

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. Dependent Data

Time Series

Spatial and Network Data

Simulation-Based Inference
IV. Causal Inference

Graphical Causal Models

Identifying Causal Effects

Causal Inference from Experiments

Estimating Causal Effects

Discovering Causal StructureAppendices

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

Proof of the Gauss-Markov Theorem

Rudimentary Graph Theory

Information Theory

Hypothesis Testing

Writing R Functions

Random Variable Generation

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

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)