This volume studies statistical inference, estimation, and data analysis. It builds on probability theory to develop methods for learning from data.
Part I. Foundations
Chapter 1. Statistical Models
1.1 Data and randomness 1.2 Parametric models 1.3 Nonparametric models 1.4 Likelihood functions 1.5 Examples
Chapter 2. Descriptive Statistics
2.1 Measures of location 2.2 Measures of spread 2.3 Data visualization 2.4 Summarization techniques 2.5 Examples
Chapter 3. Sampling and Data
3.1 Sampling methods 3.2 Bias and variance 3.3 Data quality 3.4 Experimental design overview 3.5 Examples
Part II. Estimation
Chapter 4. Point Estimation
4.1 Estimators 4.2 Bias and consistency 4.3 Efficiency 4.4 Examples 4.5 Applications
Chapter 5. Maximum Likelihood Estimation
5.1 Likelihood principle 5.2 MLE computation 5.3 Properties of MLE 5.4 Applications 5.5 Examples
Chapter 6. Bayesian Estimation
6.1 Prior and posterior distributions 6.2 Conjugate priors 6.3 Bayesian inference 6.4 Applications 6.5 Examples
Part III. Interval Estimation and Testing
Chapter 7. Confidence Intervals
7.1 Definitions 7.2 Construction methods 7.3 Properties 7.4 Applications 7.5 Examples
Chapter 8. Hypothesis Testing
8.1 Null and alternative hypotheses 8.2 Test statistics 8.3 p-values 8.4 Type I and II errors 8.5 Examples
Chapter 9. Likelihood Ratio Tests
9.1 Test construction 9.2 Asymptotic theory 9.3 Applications 9.4 Examples 9.5 Connections
Part IV. Regression and Models
Chapter 10. Linear Regression
10.1 Model formulation 10.2 Least squares 10.3 Inference 10.4 Diagnostics 10.5 Examples
Chapter 11. Generalized Linear Models
11.1 Link functions 11.2 Logistic regression 11.3 Poisson regression 11.4 Applications 11.5 Examples
Chapter 12. Nonparametric Methods
12.1 Kernel methods 12.2 Density estimation 12.3 Smoothing techniques 12.4 Applications 12.5 Examples
Part V. Multivariate Statistics
Chapter 13. Multivariate Distributions
13.1 Joint distributions 13.2 Covariance structure 13.3 Multivariate normal 13.4 Applications 13.5 Examples
Chapter 14. Principal Component Analysis
14.1 Dimensionality reduction 14.2 Eigenvalue methods 14.3 Interpretation 14.4 Applications 14.5 Examples
Chapter 15. Clustering and Classification
15.1 Clustering algorithms 15.2 Classification methods 15.3 Model evaluation 15.4 Applications 15.5 Examples
Part VI. Advanced Topics
Chapter 16. Time Series Analysis
16.1 Stationarity 16.2 ARMA models 16.3 Forecasting 16.4 Applications 16.5 Examples
Chapter 17. Bayesian Methods
17.1 Hierarchical models 17.2 Markov chain Monte Carlo 17.3 Variational inference overview 17.4 Applications 17.5 Examples
Chapter 18. High-Dimensional Statistics
18.1 Curse of dimensionality 18.2 Regularization methods 18.3 Sparse models 18.4 Applications 18.5 Examples
Part VII. Applications
Chapter 19. Data Science
19.1 Data pipelines 19.2 Model selection 19.3 Evaluation metrics 19.4 Applications 19.5 Examples
Chapter 20. Economics and Social Sciences
20.1 Econometric models 20.2 Causal inference overview 20.3 Applications 20.4 Examples 20.5 Connections
Chapter 21. Scientific Applications
21.1 Experimental data 21.2 Biological statistics 21.3 Engineering data analysis 21.4 Applications 21.5 Examples
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Statistical learning theory 22.2 Causal inference 22.3 Robust statistics 22.4 Modern developments 22.5 Emerging areas
Chapter 23. Open Problems
23.1 High-dimensional inference 23.2 Model uncertainty 23.3 Computational challenges 23.4 Data bias issues 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of statistics 24.2 Key contributors 24.3 Evolution of inference 24.4 Cross-disciplinary impact 24.5 Summary
Appendix
A. Distribution reference B. Statistical test summary C. Proof techniques checklist D. Algorithm templates E. Cross-reference to other MSC branches