Algebraic Statistics--  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 geometriy 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 completed a reasonably good rough draft of all chapters. I still need to edit everything, and provide further examples and exercises throughout. I would appreciate any feedback you have on what you read! If you have favorite examples or excersies in algebraic statistics that you think I should include, I would love to hear about them!

Algebraic Statistics (Version of December 5, 2017)

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 and Bayesian Integrals
18. MAP Estimation
19. Finite Metric Spaces