Foundations of Applied Statistics
Preface
I Introduction
1 Statistics
2 Components of Applied Statistics
3 Data Sets Used in this Book
II Expoloratory Data Analysis
4 Exploratory Data Analysis
5 Numerical Summaries of Data
6 Data Visualization Basics
7 EDA of High-Dimensional Data
8 Cluster Analysis
9 Principal Component Analysis
III Random Variables
10 Probability and Statistics
- 10.1 Central Dogma of Inference
- 10.2 Data Analysis Without Probability
11 Probability Theory
12 Random Variables
13 Discrete RVs
14 Continuous RVs
15 Joint Distributions
16 Multivariate RVs
17 Sums of Random Variables
18 Convergence of Random Variables
19 Population Principal Components Analysis
20 From Probability to Likelihood
21 Exponential Family Distributions
IV Frequentist Inference
22 Statistical Inference
23 Inference Goals and Strategies
24 Confidence Intervals
25 Hypothesis Tests
26 Maximum Likelihood Estimation
27 MLE Examples: One Sample
28 MLE Examples: Two-Samples
29 The t Distribution
30 Inference in R
31 Likelihood Ratio Tests
V Bayesian Inference
32 Likelihood Function
33 Bayesian Inference
34 Estimation
35 Classification
36 Priors
37 Theory
- 37.1 de Finetti’s Theorem
- 37.2 Admissibility
38 Empirical Bayes
VI Numerical Methods for Likelihood Functions
39 Why Numerical Methods for Likelihood
- 39.1 Challenges
- 39.2 Approaches
40 Latent Variable Models
41 EM Algorithm
42 EM Examples
43 Theory of EM
44 Variational Inference
45 Markov Chain Monte Carlo
46 MCMC Example
47 Further Reading
VII Nonparametric Statistical Inference
48 Nonparametric Statistics
49 Empirical Distribution Functions
50 Bootstrap
51 Permutation Methods
52 Goodness of Fit
53 Method of Moments
VIII Statistical Models
54 Types of Models
55 Motivating Examples
56 Simple Linear Regression
57 lm() Function in R
58 Ordinary Least Squares
59 Generalized Least Squares
- 59.1 GLS Solution
- 59.2 Other Results
60 OLS in R
61 Categorical Explanatory Variables
62 Variable Transformations
63 OLS Goodness of Fit
64 Logistic Regression
65 glm() Function in R
66 Generalized Linear Models
67 Nonparametric Regression
68 Generalized Additive Models
69 Bootstrap for Statistical Models
IX High-Dimensional Inference
70 High-Dimensional Data and Inference
71 Many Responses Model
72 Shrinkage and Empirical Bayes
73 Multiple Testing
74 Many Regressors Model
75 Ridge Regression
76 Lasso Regression
X Latent Variable Models
77 HD Latent Variable Models
78 Jackstraw
- 78.1 Procedure
- 78.2 Example: Yeast Cell Cycle
79 Surrogate Variable Analysis
- 79.1 Procedure
- 79.2 Example: Kidney Expr by Age
Appendix
References

Foundations of Applied Statistics

74 Many Regressors Model