Algebraic Statistics by Seth Sullivant.

Algebraic statistics uses tools from algebraic geometry, commutative algebra, and combinatorics to address problems in statistics and its applications. One of the main guiding principles is that statistical models are semialgebraic sets. From this observation, the geometry and algebra of the underlying statistical models can be used to get a better understanding of statistical models, analyze statistical procedures, and devise new methods for analyzing data. This book provides an introduction to this subject area, suitable for graduate courses, with background material on probability, algebra, and statistics. My guiding principle in writing the book has been to try to introduce statistical concepts and the mathematical concepts that go with them at the same time, wherever possible.

I have now submitted the final version to the publisher for copy editing.

List of Chapters

  1. Introduction
  2. Probability Primer
  3. Algebra Primer
  4. Conditional Independence
  5. Statistics Primer
  6. Exponential Families
  7. Likelihood Inference
  8. The Cone of Sufficient Statistics
  9. Fisher's Exact Test
  10. Bounds on Cell Entries
  11. Exponential Random Graph Models
  12. Design of Experiments
  13. Graphical Models
  14. Hidden Variables
  15. Phylogenetic Models
  16. Identifiability
  17. Model Selection
  18. MAP Estimation
  19. Finite Metric Spaces