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Advanced Data Analysis
from an Elementary Point of View
Cosma Rohilla Shalizi
2
For my parents
and in memory of my grandparents
17:09 Monday 30
th
January, 2017
17:09 Monday 30
th
January, 2017
Copyright ©Cosma Rohilla Shalizi; do not distribute without permission
updates at http://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/
Contents in Brief
Introduction 23
I Regression and Its Generalizations 26
1 Regression Basics 27
2 The Truth about Linear Regression 52
3 Model Evaluation 73
4 Smoothing in Regression 97
5 Simulation 127
6 The Bootstrap 140
7 Weighting and Variance 168
8 Splines 194
9 Additive Models 210
10 Testing Regression Specifications 234
11 Logistic Regression 251
12 GLMs and GAMs 281
13 Trees 289
II Distributions and Latent Structure 313
14 Density Estimation 314
3
CONTENTS IN BRIEF 4
15 Relative Distributions and Smooth Tests 339
16 Principal Components Analysis 368
17 Factor Models 393
18 Nonlinear Dimensionality Reduction 424
19 Mixture Models 450
20 Graphical Models 481
III Causal Inference 502
21 Graphical Causal Models 503
22 Identifying Causal Effects 511
23 Experimental Causal Inference 532
24 Estimating Causal Effects 538
25 Discovering Causal Structure 550
IV Dependent Data 568
26 Time Series 569
27 Spatial and Network Data 619
28 Simulation-Based Inference 629
Appendices 642
A Data-Analysis Problem Sets 642
B Linear Algebra Reminders 727
C Big O and Little o Notation 736
D Taylor Expansions 738
E Multivariate Distributions 740
F Algebra with Expectations and Variances 752
17:09 Monday 30
th
January, 2017
5 CONTENTS IN BRIEF
G Propagation of Error 755
H Optimization 757
I χ
2
and Likelihood Ratios 777
J Proof of the Gauss-Markov Theorem 780
K Rudimentary Graph Theory 782
L Information Theory 785
M More about Hypothesis Testing 786
N Programming 787
O Generating Random Variables 823
Acknowledgments 831
Bibliography 833
17:09 Monday 30
th
January, 2017
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