Advanced Linear Models for Data Science
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Advanced Linear Models for Data Science

About the Book

This book is about 50% finished. It is only available in pdf form.

Linear models are the cornerstone of statistical methodology. Perhaps more than any other tool, advanced students of statistics, biostatistics, machine learning, data science, econometrics, etcetera should spend time learning the finer grain details of this subject.

In this book, we give a brief, but rigorous treatment of advanced linear models. It is advanced in the sense that it is of level that an introductory PhD student in statistics or biostatistics would see. The material in this book is standard knowledge for any PhD in statistics or biostatistics. 

Students will need a fair amount of mathematical prerequisites before trying to undertake this class. First, is multivariate calculus and linear algebra. Especially linear algebra, since much of the early parts of linear models are direct applications of linear algebra results applied in a statistical context.In addition, some basic proof based mathematics is necessary to follow the proofs. In addition, some regression models and mathematical statistics are needed.

About the Author

Brian Caffo
Brian Caffo

Brian Caffo, PhD is a professor in the Department of Biostatistics at the Johns Hopkins Bloomberg School of Public Health. Along with Roger Peng and Jeff Leek, Dr. Caffo created the Data Science Specialization on Coursera. Dr. Caffo is leading  expert in statistics and biostatistics and is the recipient of the PECASE award, the highest honor given by the US Government for early career scientists and engineers.

Table of Contents

  1. Introduction
  2. Background
  3. Single parameters
  4. Linear regression
  5. Least Squares
  6. Examples
  7. Bases
  8. Residuals
  9. Expectations
  10. Normal distribution
  11. Distributional results
  12. Residuals and diagnostics
  13. Under and overfitting
  14. Penalties
  15. Asymptotics
  16. Mixed models

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