Advanced Statistical Methods: A Disciplined Guide to Data Analysis with R

About the Book

Move beyond foundational concepts and dive deep into the quantitative heart of data science with this comprehensive guide to advanced statistical methods. Advanced Statistical Methods: Data Analysis with R is a practical and disciplined resource that equips experienced data professionals with the rigorous analytical techniques needed to unlock deeper insights and build robust, evidence-based models.

With a hands-on approach using the R programming language, this book transforms raw data into reliable knowledge, covering everything from regression and Bayesian statistics to knowledge discovery methods. All research and references within the text adhere to APA citation standards, ensuring a foundation of professional and academic rigor.

Target Audience & Prerequisites

This book is ideal for a more advanced audience seeking to deepen their technical and analytical skills. It is especially well-suited for:

Experienced Data Analysts and Scientists: Professionals looking to master more sophisticated statistical methods for their daily work.
Graduate Students and Researchers: Individuals requiring a practical guide to applying advanced statistical concepts in R.
Quantitative Professionals: Anyone who needs to move beyond elementary analysis to build more complex, defensible models.

A foundational understanding of statistics and a basic familiarity with R are recommended.

Full Table of Contents

Introduction to R
- Feature Comparison
- Big Data Analysis
- Big Data Analytics
- What about Python?
Data Analysis and the Development Environment
- Supervised Machine Learning
- Importance of Random Sampling
- Large Data Sets with Little Explained Variance
- Prediction Using Large Data Sets
- Caveats
- Development Environment
- Notebook Configuration
- Analyzing the Birth Dataset
Regression Analysis
- Linear Models
  - Strategy 1: Brute Force Polynomial Expansion
  - Strategy 2: Correlation and Covariance Matrices
  - Implementation
- Multivariate Models
  - Multilinear Regression
  - Regression and Histograms
- Logistic Regression and Parsimony
  - Fitting a Logistic Regression Model
  - Parsimony and Principal Components
  - Parsimony and Big Data Analysis
  - Overfitting and Least Squares
  - Principal Component Analysis
  - Categorical Variables and Logistic Predictions
  - Predicting Outcomes with Logistic Regression
Bayesian Statistics
- Frequentist versus Bayesian
- Cases for Bayesian Models
- Pachinko Prediction
- Alternative Bayesian Applications to Social Media
Knowledge Discovery
- Distance Metrics
- Determining Optimal Cluster Size (Elbow ‘Method, Averaging Silhouettes, The Gap Statistic)
- K-means != k-Nearest Neighbors
- Ensemble Methods (Bayesian Voting, Random Forest)
- Association Rule Mining (Market Basket Analysis)
Appendix
- Life Expectancy by State
- Median Home Price by City (Color)
- Maximize Accuracy versus Minimize Misclassification
- Fitting a Bayesian Logistic Regression Model
- References

From the Author

For those who have mastered the basics, the next level of data analysis requires a deeper, more rigorous understanding of the quantitative methods that power our insights. I wrote this book to provide that next step. It is a guide for moving from simply running analysis to truly mastering the statistical principles behind it, all within the flexible and powerful R environment. My goal is to equip you with the advanced knowledge to build more complex, defensible models and to transform your data practice from a craft into a science.

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Elevate your analytical skills and master the advanced statistical methods that drive true data insight.

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